A family friend of William Bradford Bishop Jr., the former State Department official who allegedly killed five members of his family in 1976 and then vainshed, told Swedish police that she saw Bishop in the streets of Stockholm on two separate occasions last July.

The woman's report of sighting Bishop has prompted a six-month investigation by Swedish police and the FBI, which sent an agent to Stockholm to aid in the search.

Although there have been a number of reported sightings of Bishop in three years since he disappeared, "this is the first solid one," one police official said last night.

The woman, whose name is being withheld by authorities, "knew (Bishop) well when he served with the State Department in Africa" in the mid-1960s, according to a statement released yesterday by the FBI field office in Baltimore. Reportedly she told police that Bishop was wearing a beard.

The last known contact with Bishop occurred March 2, 1976, when Bishop used a credit card to buy supplies in a sporting goods store in Jacksonville, N.C.

Earlier in that day, the beaten bodies of Biship's wife, mother and three sons had been found in a shallow grave about 100 miles north of Jacksonville in a rural North Carolina swamp. The bodies had been doused with gasoline and set afire, and the smoke led a forest ranger to the site.

It took police nearly a week to identify the victims, and then to confirm that the fatal beatings had occurred on March 1, in the Bishops' home in the Carderock Springs subdivision of Bethesda.

Maj. Wayne G. Brown of the Montgomery County Police Department said yesterday that unlike dozens of previous reports on Bishop's possible wherebouts "this apparently is a good sighting." Brown, the chief of criminal investigation in Montgomery, said the FBI told him they are taking the woman's story "very seriously."

However, the FBI's official statement, that "the individual making the report of the sightings was not in a position to be sure Bishop was spotted."

It went on to say that "Swedish police are cooperating with the FBI and the U.S. Embassy in Stockholm in efforts to locate and possibly identify the subject."

In the nearly three years since the killings, police have checked out hundreds of reports that Biship had been seen, in this country and in Africa and Europe.But this latest tip was the first to come from someone who was a friend of Bishop and his family.

An FBI spokesman in Baltimore said agents from the agency's European staff have been conferring with Swedish police for some time. The latest meeting took place yesterday in Stockholm with an agent from the FBI's London office.

Gary Reals, a reporter for WMAL radio, said last night from Stockholm that the Woman ho made the reports was a Swedish national who was living in Addis Ababa, Ethophia, when Bishop was stationed there in the mid-1960s.

Reals reported that Swedish police have been conducting a covert investigation for the past six months, but are resisting pleas by American officials to distribute a photograph of Bishop to the news media in Sweden.

The Sightings occurred during the first week in July 1978, according to the FBI.

Brown, whose department turned the search over to the FBI after murder indictments were returned against Bishop, said no one from the Montgomery County force would go to Sweden "because the FBI has jurisdiction under an unlawful flight warrant."

The name of the woman who allegedly saw Bishop was not released.

Reals said she is believed to have been a close friend of the Bishop family during their stay in Ethiopia. Reals said the woman was either an employer or married to an employe of the Swedish embassy in Addis Ababa at the time, or possibly was married to an Ethiopian.

Several American diplomats who were stationed in Ethiopia with Bishop said last night they could not recall any Swedish woman, but one added, "the Bishops were a gregarious family who enterntained many people in their home."

Bishop, who is 42, is charged with the murders of his mother, Lobelia, 68, his wife, Annette, 37; and sons Brad III, 14, Brent, 10, and Georffrey, 5.

At the time of the killings, Bishop was a highly regarded career diplomat who had held diplomatic posts in Italy and Botswana, in addition to Ethopia. A graduate of Yale who also held master's degrees from both Middlebury College and UCLA, Bishop speaks fluent Ialian and Srrbo-Croatian.

Bishop's station wagon was recovered 18 days after the slayings at a compground deep in the Great Smoky National Park on the North Carolina-Tennessee border.