Two area chiropractors, seeking to break a tradition against members of their profession working beside medical doctors in hospitals, are petitioning Alexandria Hospital for permission to admit and treat patients there. Both have threatened to sue the hospital if their request is denied.

The application from Alan L. Tannenbaum of Alexandria and L. Richard Vaitsas of Winchester, Va., has been opposed by a doctors' committee at the hospital on the grounds that medical doctors do not understand chiropractic treatment and could not supervise its application, according to a hospital spokesman.

"When a patient goes to a hospital, he should have a choice of the types of doctors he sees and types of services he receives," said Tannenbaum, 29, who first approached the hospital in January 1982.

At a four-hour closed meeting Tuesday night, members of the hospital's board of directors closely questioned the two chiropractors on their training and medical philosophies, according to Tannenbaum and his lawyer, Bernhardt Wruble. A spokesman for the hospital said no date has been set for a final decision by the board.

Federal policy toward chiropractors is in flux, with the Department of Health and Human Services having proposed changes in eligibility rules for the Medicaid and Medicare programs that would tend to give chiropractors more standing at hospitals.

The Joint Commission on Accreditation of Hospitals, a private group that sets and administers hospital standards, also is rewriting rules that now tend to bar chiropractors from full-time staff positions so as to give the hospitals more flexibility.

The country's 22,000 licensed chiropractors specialize in manipulating the spine and neck to relieve pain and other disorders. For years, chiropractors have charged that their profession is unfairly demeaned by medical doctors and portrayed as a "unscientific cult," even though it requires four years at a chiropractic college and licensing from the state.

American Medical Association official policy states that the "unscientific cult" label is unwarranted, but that chiropractic treatment is ineffective against many ailments.

With a few exceptions, chiropractors do not have rights to admit patients to hospitals across the country, which many see as an unfair restraint on their profession.

The feud has generated lawsuits over the years. Five chiropractors unsuccessfully sued the AMA and other medical organizations for alleged violations of federal antitrust laws by restraining the chiropractic practice.

Tannenbaum says that under the current rules, he cannot admit a patient who needs the specialized X-ray and laboratory services available at Alexandria Hospital. If the patient is admitted, a medical doctor must perform the treatment and Tannenbaum can come in only as a visitor.

Last year, Tannenbaum says, he was told by a committee representing doctors at the hospital that the services he could perform could be handled by other members of the staff and that there was a "philsophical" difference between medical doctors and chiropractors that could not be resolved.

Hospital attorney Thomas C. Brown Jr. said the medical doctors' objections to the chiropractors was based on training differences. He said doctors asked "How can medical physicians who are not trained in chiropractic supervise the activities of chiropractors and be ultimately responsible for the care of their patients?"

Tannenbaum says his training is similar to the doctors' and that the real reason for the objections is that the doctors see the chiropractors as competition for business.