Agnes Mongan, 73, this year's Kress Professor in Residence at the National Gallery of Art - the first female so honored - has a crisply regal manner, a voice like Katherine Hepburn's and hair as white as snow. A connoisseur of drawings, and of art connoisseurs, she is among the most influential, and the most beloved, teaching art historians of her time.The curatorial offices of America's museums are stocked with scholars she helped train.

She is fastidious, imposing. When she says "I am no women's libber," there is in her assertion no hint of passivity. Mongan years ago selected another style. There is no smoking in her presence; it simply is not done. "She has this thing for 'gentlemen,'" says one of her colleagues, and her preference is apparent. "You may have heard," she says, "that I am called the ogre-ette." It is true that she intimidates, but through fineness, not through fierceness. She knows her lady's rights.

In a field ruled for years by men, many wealthy or high-born, Mongan, who is neither, nonetheless attained much in her profession. So did her equally well-known sister, Betty, now retired. Agnes studied drawings, Betty worked with prints. When specialists in graphics cite a paper by Miss Mongan, the often-heard response is "Which one? A or B?"

The Mongan family is Irish, and in the neighborhood of Harvard Yard such things used to matter. Agnes Mongan had no Ph.D., and such things matter sill, but she was the first woman to be named director of Harvard's Fogg Art Museum. The post did not come quickly. She worked there 40 years.

"I remember when, as curator of drawings there, I was paid half as much as my male counterpart, the curator of prints. Of course they discriminated against women. When I dined at the Harvard facutly club, I could not use the front door. I say I am no libber, but without the heightened feelings, all the recent rumblings, I would not be here."

Her male colleagues at the Gallery strenuously deny that. "Miss Mongan used to say that in order to succeed a woman merely had to be better than the men," says one of her former students. "She was. That's why she's here."

There is another reason. If there is an old boy network in America's museums, Mongan is part of it. "I did not teach Carter," she says of Carter Brown, the National Gallery's director, 'but I knew his parents before he was born." It is said that she knows everyone, and in half an hour's conversation the acquaintances she mentions include Bernard Berenson, Indira Gandhi, Alexander Calder, George Balanchine and the king of Sweden.

Of course she knows the people who run the big museums. The National Gallery, the National Portrait Gallery, the Museum of Modern Art, the Metropolitan, the Albright-Knox, the Wadsworth Atheneum, the Boston, the Chicago - they all have had directors who were Harvard-trained.

In the study of fine arts, Harvard represents a particular tradition. Connoisseurship rules there. Slides and photo archives are frown on at the Fogg. Harvard students are, instead, exposed from the start to works of art themselves. They are taught that objects are more important than their sources, that a picture's sensuous presence matters more than its iconographic content. This attitude towards objects, which Mongan manifests, reaches back through Harvard to John Ruskin and beyond.

So does the old boy network which helped bring Agnes Mongan to the National Gallery of Art.

She worked for years, first as student, then as ally, with Prof. Paul J. Sachs, the legendary, tiny, connoisseur-collector. Sachs, in turn, was partly trained by Charles Eliot Norton, Harvard's very first professor of fine arts. In March, in order to fulfill her Kress professorship duty, Miss Mongan will lecture at the Gallery on "Visitors to Venice," one of whom was Norton.

Norton was born in 1827. He knew everyone! Ruskin, Dickens, Carlyle. The world seems small today, it was even smaller then. And it was as closely knit in the 18th century, and the 17th, they all knew each other, too. This is an absolutely straight line from the 16th century on."

Berenson is on that line; Mongan knew him well. So is Kenneth Clark, whom Mongan met in 1929. And the students she has trained extend the old boy network. "I remember the first time that I saw her," says the gallery's Earl A. Powell III. "I'd just enrolled at Harvard. I'd come out of the Navy, cold. At that time at the Fogg she was helping teach Fine Arts 200, 'Criticism and Connoisseurship.' She began by showing us the proper way to handle works of art. She walked into the room, peered into our faces, and pulled on her white gloves."

Alice Mongan, who was born "eight-tenths of a mile from Harvard Square" and graduated from Bryn Mawr in 1927, voices strong opinions, and teaches as she talks.

"I cannot stand," she said, "museums without natural light. It is one of my pet phobias. Recently I visited 11 new museums; eight relied entirely on artificial light. I wanted to scream. If you spotlight sculpture, you rob it of its light. People have been taught that daylight ruins pictures. Nonsense," said Miss Mongan. "I wish you would tell your readers to insist on natural light. And they should mistrust slides. Have them look at objects. And tell them not to smoke."

As befits a connoisseur, her art knowledge is both general and specific. She speaks as confidently about the history of paper and the qualities of chalk as she does on beauty. While at the Gallery she will continue to write articles and catalog (she is working now on Ingres, that most meticulous of draftsmen). She also lends advice on acquisitions and exhibits to the museum's staff.

In her office at the Gallery a borrowed painting by Degas hangs behind her desk. The loupe she always wears is suspended from her neck on a chain of woven gold. The rosette at her collar represents the "Palms d'Academie," an honor she was given by the French in 1949. The book that she is reading was printed in 1792. "It is true that I am the first woman to be appointed Kress Professor. I think it even more interesting that I am only the second native-born American, don't you?," asks Agnes Mongan.