Fairfax Hospital Association, a nonprofit organization that operates Fairfax County's three largest hospitals, yesterday took control of the privately owned Jefferson Memorial Hospital in Alexandria.

The move marks the association's first venture outside Fairfax, as well as a major change for Jefferson Memorial, which has been run for the past three years by a for-profit health-care group based in Memphis.

Officials at the association, which signed a 20-year lease to run Jefferson Memorial effective yesterday, said they had no immediate plans for major changes.

They said that the 120-bed hospital would benefit in the long run by referrals from other association programs and facilities in Northern Virginia.

"We believe that cost-efficient health care with a local community base will continue to become increasingly important," said J. Knox Singleton, Fairfax Hospital Association's president.

He said the group's control of Jefferson Memorial "will help to assure the community that it is provided."

Although Jefferson Memorial, located on the Arlington-Alexandria border near Baileys Crossroads, said it recorded profits of about $520,000 last year, the number of patients there slipped by 28 percent from 1982 to 1984.

Area health-care officials said that drop reflects a national trend toward declining bed-occupancy rates for hospitals.

Partly because of shifts in federal reimbursement policies for hospitals and the availability of new alternatives to hospitalization, patients have increasingly sought treatment as outpatients.

The association operates a number of programs that offer health care outside its hospitals. Jefferson Memorial officials are hoping the programs, which include treatment for alcoholics and home-health care, will lead to new patients at the hospital.

Jefferson Memorial Hospital is owned by a group of about 15 investors led by Dr. Laszlo N. Tauber, medical director and chief of surgery at the hospital.

Tauber said yesterday that under the new agreement, FHA will pay the investors $1.37 million in annual rent until 1987, when the sum will rise to $1.62 million. In 1992, the rent will rise to $2.12 million.

A floor that was built on to the hospital two years ago for office space and currently vacant, will also be controlled by the association under the contract.

Under the previous contract, Health Group Inc. of Nashville paid the investors $1 million a year, which was to have increased to $1.25 million in 1987.

Health Group, which did not control the additional floor of office space, is in the process of liquidating its assets, according to a company spokesman in Nashville.

Jefferson Memorial, which opened in 1965, provides a range of basic hospital services, including a small intensive-care unit.

The hospital draws patients from Alexandria, Arlington, Falls Church and eastern Fairfax County.

The association already operates the Fairfax Hospital on Gallows Road in central Fairfax, Commonwealth Hospital in Fairfax City and Mount Vernon Hospital in eastern Fairfax.

The association is presently building a new hospital near Fair Oaks Mall, which will replace Commonwealth.

Donald L. Harris, senior vice president of the association, said any profits generated by Jefferson Memorial will be put back into the hospital. Harris said he did not yet know what improvements will be made, but he added that major renovations or expansions are not likely in the near term.

Richard A. Levy, administrator of Jefferson Memorial, said it was possible that the association, which will be able to provide the hospital with economies of scale, can keep prices from rising sharply.

"It's possible that there will be a slower increase in prices than what might be anticipated otherwise," Levy said.

"We stand to benefit from this association with FHA," he added.