The bodies of a man and woman who apparently had been shot to death were found yesterday in an Alexandria high-rise apartment after neighbors noticed blood dripping from a balcony.

The man was identified tentatively as Dr. Herbert J. Mueller, 57, a Navy Department physicist and research executive. The woman was believed to be his wife, Louise.

Police said the woman was found in a bedroom and the man on a balcony of the seventh-floor apartment at 4801 Kenmore Ave. A handgun was found on the balcony.

There was no indication that the contents of the apartment had been disturbed and witnesses said the door was chained shut from the inside. Police said they are still investigating the matter but are not now seeking any suspects.

Authorities declined to speculate on a motive for the shootings or release further details. They said they could not make positive identification of the victims before the arrival here of the Mueller's son, who lives in Canada.

Colleagues described Dr. Mueller as director of research and acting chief scientist for the Naval Air Systems Command, which he joined in the late 1960s after carrying out research on chemical explosives for the Army in Fort Belvoir.

One longtime associate said that for the last three months, Mueller, who was born and trained in Vienna, Austria, had been carrying particularly heavy work responsibilities, supervising his own unit and acting as temporary manager for another division.

The associate said Dr. Mueller told him Friday that he planned to work at home over the weekend on his department's budget.

Police said they were called, along with rescue personnel, to the Muellers' apartment about 1:40 p.m. after the dripping blood was discovered. They said they did not know just when the shootings occurred, although an undisturbed Sunday newspaper was found outside the apartment door. a