Nancy Hanks, 55, the highly regarded head of the National Endowment for the Arts and the National Council on the Arts for eight years before resigning in 1977, died Jan. 7 in Columbia Presbyterian Hospital in New York City where she was being treated for cancer. She lived in Washington.

During her years as chairman of the Endowment, she saw federal appropriations for her agency rise from $11 million to $114 million, with the number of grants increasing from 711 to more than 5,000. These grants helped subsidize thousands of organizations involved in architecture, theater, film-making, dance, music and poetry.

Many of those grants went for new experimental activities and organizations, and to community-oriented projects. The Endowment sponsored teaching programs for black poets and authors to teach in inner-city schools, gave funds to small communities for the purchase of art works, and helped fund the travel of opera, theater, and dance groups to small towns across the country.

Besides monies appropriated by Congress, the Endowment encouraged contributions by private industry and foundations. Many of the grants to local and state arts groups were in the form of "matching" or "challenge" grants, and were made contingent upon those groups getting equal or greater sums of money from the private sector. Miss Hanks once estimated that for each dollar the federal government spent through her agency, another three were raised in matching funds.

Miss Hanks gained a reputation as a dynamic administrator, as well as a forceful advocate for the arts on Capitol Hill. She gained a reputation as one administrator who could get what she wanted in the bloody appropriations fights in Congress.

She had a habit of reminding elected officials that support for the arts paid off politically. With grants going to virtually every community of any size, rather than simply to large organizations in a few large states, the number of persons interested in arts appropriations, as well as their geographic diversity, increased dramatically.

After Miss Hanks announced in 1977 that she was retiring, The Post said in an editorial that "Miss Hanks brought the NEA from relative obscurity to a position of great influence over a wide range of cultural activity in this country. She made it look easy, as she threaded her way through the cultural minefields in Congress and the bureaucracies with precision and sophistication. All those who are involved in or merely care for the development of the arts in this country are heavily in her debt."

Since leaving the government, she had been a vice chairman of the Rockefeller Brothers Fund. She also served on presidential task forces dealing with the arts for President Reagan. She was a trustee and member of the executive committee of Duke University. She was a regent of the Smithsonian Institution, and held its Smithson Medal. She also had received awards from the city of New York and the National Symphony League.

Miss Hanks was born in Miami Beach and reared in Florida and New Jersey. She was graduated magna cum laude with a degree in political science from Duke University in 1949. While there, she had been a May queen, head of the student government, and member of Phi Beta Kappa. She also studied geology at the University of Colorado and political science at Oxford University.

She moved to Washington in 1951, and took a job as a receptionist with the Office of Defense Mobilization. A year later she became a secretary with the President's Advisory Committee on Government Operations, chaired by Nelson A. Rockefeller. When Rockefeller became undersecretary of Health, Education, and Welfare, Miss Hanks became his secretary. In 1955, she became his special assistant in the Special Projects Office of the White House. Miss Hanks went to New York in 1956, where she directed studies for the Rockefeller Brothers in fields ranging from foreign policy and defense to economics and education. In the mid-1960s, she directed a study on the problems of the arts in this country. Published by McGraw-Hill in 1965, it was hailed as the first comprehensive treatment of the subject in the United States. She continued to work for the Rockefellers until named to succeed Roger L. Stevens as head of the Endowment in 1969.

Survivors include her mother, Virginia Wooding Hanks of Washington.