The Virginia Supreme Court gave Fairfax County prosecutors two major victories today in their efforts to crack down on illegal activities at adult bookstores in the county.

The court ruled that a Fairfax Circuit Court judge was wrong when she refused to close a Mount Vernon adult bookstore after holding that illegal sexual encounters there were creating a public nuisance. In a second decision, the court upheld nine obscenity convictions against another Fairfax adult bookstore.

The first ruling upheld Fairfax prosecutors' attempts to close Croatan Books Inc. under a public nuisance law previously used to shut houses of prostitution and massage parlors. Although the court's decision today came almost four months after the store in the Mount Vernon area had been closed by its owner, prosectors said the decision will offer a new avenue to law officers trying to curb illegal activities elsewhere.

"Other parts of the country have seen the same pattern," said Fairfax Commonwealth's Attorney Robert F. Horan Jr. "What starts out as a bookstore winds up a place of assignation where people come to engage in sexual activity."

The state court said that Fairfax Circuit Judge Barbara M. Keenan had the authority under the state's police powers to order the store closed. Keenan ruled in August 1983 that while illegal homosexual activities occurred in the store, she believed the closing law was unconstitutional because it violated the store's First Amendment rights.

The state court disagreed in an unanimous ruling. "The governmental interest in eliminating a pattern of criminal sexual activity is unrelated to the suppression of free expression," the justices said in a 10-page decision.

Attorneys for both the defunct Showplace Books and Educational Books Inc., the last remaining adult book shop in Fairfax County, have attacked court decisions against the stores, saying the decisions infringe on free speech rights.

The Supreme Court also upheld nine convictions against Educational Books on charges of selling obscene magazines, tossing aside the store's contention that seven of the convictions violated its constitutional protections against double jeopardy because nine of the items were purchased during only two visits to the store.