Eve Arnold and Inge Morath were the first - and for some time the only - women members of the distinguished Magnum photographic agency. Sharing a sensibility to the extraordinary-in-the-ordinary around the world, they could have been rivals. But on the day they met in Magnum's New York offices in 1956, they struck up a friendship that has lasted a lifetime. Here the photographers pay tribute to each other's life and art

Inge Morath on Eve Arnold

I first met Eve Arnold in New York. I think it was in 1956, the occasion was a Magnum meeting. It was really my first longer trip to New York; I lived in Paris and American ways were unknown to me and strange. Television had not yet brought everybody's living room into your own, the mysteries of New York had to be discovered by oneself. It was a little overpowering and I was extremely happy when Eve Arnold invited Henri Cartier-Bresson - with whom I was working at the time - and me to come out to her house in Port Jefferson on Long Island and spend a Sunday. That was the day I fell in love with Eve's way of being, with her quiet generosity of spirit and her lavish spoiling of her friends. The brunch that she prepared for Henri and me that day is a thing that firmly sticks in my mind. I did not really know what brunch is. There was, at midday, this gorgeous spread of shapes and tastes I had never seen in these combinations. We must have eaten a lot because we took a long walk on the beach in the afternoon, finding pieces of coloured glass polished like gems by the ocean. There was no formality, only openness, no competition but a wish to share. Later, we looked at some of the photographs Eve had taken of the people and the town she lived in, touching in their humanity and beautiful in their form, a magic introduction to her country.

I tell of this first day together at length because all our further encounters had that same spirit. We worked in many different places in many parts of the world, we worked within that special group of our fellow Magnum photographers - all of whom at that time were men - and enjoyed it. But something like a special bond remains, there is some feminine understanding and appreciation of each other's ways of being, and of seeing, that I treasure. Thank you, Eve.

Eve Arnold on Inge Morath Long before I met Inge Morath (was it 1956?), she engaged my imagination. I had seen her early photographs and found them beautiful in their deceptive simplicity. Actually, they contained a great deal of information and were highly sophisticated - hers was a European sensibility that intrigued me.

Then, late one summer's night, I checked into a tacky little hotel (called the Little Hotel, $3 a night) near the Magnum office in New York. As I walked down the dimly lit hall, I tripped over a stunning pair of grey leather Belgian shoes which had (European style) been put out for polishing. I smiled to myself, thinking I hope nobody steals them in this flea pit, and I wondered about the wearer.

Next morning, when I walked into the Magnum office, there was Inge Morath standing in the grey shoes. In those days, she was dressed by Balenciaga so the rest of her looked exquisite, too.

In the beginning, as the only two women among an overwhelming majority of men, we formed a bond and over the years I have enjoyed her friendship, her affection, her delightful giggle, her humour and her grace. Whatever she does is done with style, intelligence and skill. Before she went to Russia, she learned the language - and when she went to China, she was able to read the poetry. I have learnt a great deal from her.

Is it any wonder that I cherish her friendship?

`Eve Arnold, Inge Morath: Women to Women', an exhibition of photographs, is at the Mappin Gallery, Sheffield, from 15 March-26 April (0114 276 8588)

Worlds and pictures (clockwise from top left): Eve Arnold's 1965 photograph of a meeting of Brides of Christ on their wedding day to the Lord, Godalming, Surrey; and a bar girl in a Havana brothel, 1954; the Feria de Sevilla (spring fair), 1987, by Inge Morath; car passengers wearing Saul Steinberg masks, USA 1962; and dancing bedouins, south of Baghdad, 1956, both by Inge Morath