I do not think that Jackie Kennedy was present for much of the time, for she was not a great campaigner, nor indeed very keen on politics in any form. And she was pregnant. However she was present at the final meeting, which, ironically in view of future events, took place in front of the so-called Freedom Hotel in West Harlem, into which Fidel Castro had previously moved for a United Nations session, because his entourage was not allowed to pluck its chickens at the Waldorf-Astoria.

That meeting was addressed by one of the most memorable collection of speakers I have ever heard: Mrs Roosevelt; old Senator Lehmann, the epitome of liberal Jewish New York; the Rev Adam Clayton Powell, a black local Congressman who was stronger on tub-thumping than on devoutness; and the Presidential candidate John F. Kennedy. The oratory was to me both bizarre and mesmeric.

Visually, however, it was Mrs Kennedy, at once demure and dazzling, who stole much of the show. During the 34 months of the Kennedy presidency, I came through mutual friends to know her somewhat. But it was only after the assassination that I knew her at all well.

I remember on a very hot evening in 1965, at an F. Scott-Fitzgerald-like house on Long Island Sound, playing with her one of my last singles sets of tennis. Very soon afterwards I decided that it was only doubles for me, but that was not because of the fierceness of her game. She was an exceptionally bad tennis player, maybe because of a reaction against Kennedy competitiveness, and even I had to try quite hard to lose a couple of games.

She was a loyal supporter of her husband's family, and spontaneously close to Bobby Kennedy during the four-and-a-half years between the two assassinations, but she always stood back a little from the stockade athleticism of the Kennedys, a more zestful version of the Isle of Wight activities of the Bottomley clan, and brought up her own daughter and son who could hardly have had a more intimidating start than as the children of an assassinated President and most famous widow in the world with a quiet fastidiousness as successful as it was perceptive.

I hardly saw her during the Onassis marriage, but then came back to an intermittent friendship during the last two decades. In earlier years there had been a certain revolving lighthouse quality to her. Sometimes the beam would flash forth with dazzling brightness, then it would turn away again. But as the sense of appalling exposure (not to physical danger, but to an inquisitive and unmerciful world) gradually faded when the horror of 1963 receded, so she became less defensive and lived an increasingly normal, though hardly average, New York life.

She worked seriously as an art publisher's editor, a job she did part-time but by no means in an amateur or frivolous way. I retain two particularly vivid memories from the last ten years. One is of a long train journey from Euston to Bangor, for David Harlech's funeral following his fatal motor crash in 1985. (There was always a lot of tragic and sudden death about both the Kennedys and the Harlechs, which was perhaps one of the things which held them together and made him such a successful Ambassador to Washington in the "Camelot years"). There was a strong Kennedy representation, including Senator Ted and Jean Smith, now the American Ambassador in Dublin. With the two of us, we were six at adjacent tables in the restaurant car, and I suppose attracting some attention.

Suddenly Jackie was seized with admiration for the English countryside (it was a bright day, though the London to Crewe route is hardly the most scenic in Britain), and sought to put her other English countryside memories into geographical perspective.

"Where's Chatsworth?" she said in her low, slightly breathless voice. I pointed vaguely northward. "And where's Badminton?" I switched to an equally vague south-westerly direction. "And where's Birch Grove?" (Harold Macmillan was still alive, but the scale of housing was descending.) I pointed backwards down the train. And then after a longer pause, and going much further down the scale, "And where's East Hendred?" (our house near Wantage). Whereupon, almost before I could get in my final southerly point, we all dissolved into the uncontrollable laughter which is not incompatible with sad journeys.

The second memory is more recent. In 1991, she and her nice, comfortable, intelligent diamond-merchant friend, Maurice Tempelsman, came for Oxford Encaenia. She gave the impression of enjoying everything, the Sheldonian ceremony, even with its uncomfortably-backed seats, the Latin, the All Souls luncheon despite not nominally being one of the stars, which is to say she did not get a degree, although she was inevitably the star attraction at the post-ceremony festivities. On the next day I had a few of her old friends to lunch with her at the House of Lords, which she wanted to see. After it and a quick visit to the gallery we stood in the lobby while one or two people came up. For quite a long time we were a quartet: Jackie, Archbishop Runcie (who was a great success), Solly Zuckerman (who had been at the lunch) and me.

When she got back to New York, she wrote an enchanting thank-you letter saying that her idea of heaven was to stand perpetually in the lobby of the House of Lords chatting with this group. I discovered subsequently that she had used the same thought, with the locale transferred to the courtyard of Hradcany Castle, in a letter to President Havel. But I did not blame her in the least for that. If I had found such a felicitous phrase I would certainly have used it more than once, and it was good for me to be taken down a peg. In any event, whatever her real heavenly preference may have been, I hope that she finds it.

She was very brave ("when I think of all the time I wasted on those wretched press-ups", she said when told of the nature of her illness). She was discriminating. She obviously had unique style. And she gave great pleasure to others.

Arthur Schlesinger, Jnr: She was a woman of fierce independence. Of course she was famously beautiful and elegant, and she fascinated and enchanted her age. But one recalls above all the quiet but implacable determination, amid the uncontrollable blazes of publicity, to live her own life.

Her father, Black Jack Bouvier, was a swashbuckler. Her mother was a very proper society matron. She was brought up at a time the 1940s and in a place, Newport, where young ladies were taught to conceal their intelligence lest it frighten young men away.

She observed the conventions, but underneath a shy exterior developed cool judgment of people and an ironical slant on life.

In the early 1950s, she met another ironist, John Fitzgerald Kennedy. Their marriage was a notable moment in the social history of the United States: at last the Irish were accepted in Newport.

Jacqueline Kennedy took to her new political life more easily than her Newport friends expected. Like her husband, she was an idealist, and, like him, an idealist without illusions. She came to like politicians and their free and easy talk, and she came rather to like campaigning.

Bursting upon the electorate in 1960, the handsome couple seemed the embodiment of youth, and rather daring in a nation ruled by tired old men. She added more than decoration. Jack Kennedy always sought her assessments of people, and sometimes asked her to carry out confidential missions. When, for example, he wanted to talk to John Kenneth Galbraith and me, but did not want to disquiet his possessive and overworked campaign staff, Jacqueline would make the call and set up the meeting.

Once her husband had been elected President, she wondered how she could best play her role as presidential wife (she detested the term First Lady, regarding it as undemocratic). Her expertise lay in the arts, and her aim was to use the White House to honour artistic achievement. Soon Casals, Stravinsky, Robert Frost, Isaiah Berlin and Leonard Bernstein were presidential guests.

Jackie saw the White House itself not as a private residence but as a possession of the American people, and she very efficienctly organized a redecoration and refurnishing designed to renew the historical continuities. To those of us on the White House staff, the Kennedys appeared an affectionate couple, delighting in each other and their two attractive children. No one can know the inwardness of a marriage, but despite latterday tales of women parading through the White House, theirs seemed increasingly close.

The President could be a solicitous husband. I remember his asking me, after the loss of their third child, whether I could get Adlai Stevenson to send a note of condolence: "Jackie is very fond of Adlai, and hasn't heard a word from him."

Then came Dallas. In the dark weeks and months afterward, Jacqueline and her brother-in-law, Robert, were drawn together in grief. He became the protective element in her life. Seeking privacy for her children and for herself, she moved to New York and began a new career as an editor in a publishing house, a job for which her critical eye and flawless taste admirably equipped her.

She was proud of Robert Kennedy in his opposition to the war in Vietnam, but hated it when he decided to run for President. "They will do to him what they did to Jack," she said to me in March 1968. In June, "they" did as she predicted.

Three months later, seeking a new protection, she married Aristotle Onassis. After Onassis died, Jacqueline returned to her quiet, highly disciplined life: winter in New York; riding in New Jersey or Virginia in spring and autumn; summer in Martha's Vineyard.

An excellent mother, she raised unspoilt children and taught them how to elude the paparazzi. Both are lawyers; Caroline has co-authored a book on the Bill of Rights and now has three children of her own.

In her middle years, Jacqueline was more fascinating than ever. Her finely modelled face resisted age. She always had the seductive habit of giving undivided attention to the person with whom she was talking. Her humour gleamed, and her zest for life never flagged. She was a great reader and loved the theatre. She followed politics and remained an ardent, liberal Democrat to the end.

In 1992 she acquired a new friend in Hillary Rodham Clinton. They lunched together a couple of times during the campaign, hit it off at once, and kept in close touch thereafter.

The illness struck unexpectedly last December. Doctors diagnosed it as lymphoma in January. She seemed cheery and hopeful, perhaps to keep up the spirits of her friends.

"I feel it is a kind of hubris," she told me. "I have always been proud of keeping so fit. I swim, and I jog, and I do my push-ups, and walk around the reservoir, and I gave up smoking forty years ago and now this suddenly happens." She laughed as she talked. Chemotherapy, she added, was not too bad; she could read a book while it was administered.

The doctors said that in 50 per cent of cases lymphoma could be stabilised. She bore the last ordeal with characteristic gallantry, and with never a word of complaint. She died as she lived, in grace and in dignity "a very classy dame", as they say in New York.

Henry James would have understood her, and could have portrayed her. She will be remembered as the American woman at her best: brave, disciplined, ironical, imperturbable, filled with a vivid sense of the potentiality and the sadness of life.