One day in the fall of 1981, Georgiv V. Veremey, a first secretary at the Soviet Embassy, walked into the offices of Software AG of North America in Reston, which keeps a sophisticated computer software system called the "Source" in a 1,500 pound safe on the 11th floor.

Veremey walked past a receptionist and straight to a clerk who handles mail orders in a back office. "It's a mystery how he knew where to go," says company president John Maguire.

Veremey, who has been identified by the FBI as an officer in the Soviet military intelligence, the GRU, "was extremely vague about the nature of his work with the Soviet Embassy," according to Maguire. When Veremey asked for a variety of manuals describing Software's products, he was sent away with a blank order form.

Undiscouraged, Veremey returned a week later but was told it was company policy not to sell to the Soviet Union. A few months earlier, a Belgian businessman acting on behalf of the Soviets, had offered Maguire $450,000 under the table for a copy of the "Source." Maguire notified the FBI and the agent was arrested.

Software's experiences illustrate the Soviets' intensive pursuit of American technological secrets, an effort that led Sen. Sam Nunn (D-Ga.) to conclude: "The Soviets have come to view our technology as their technology, to be obtained whenever they need it."

In this effort, the KGB plays a crucial role, according to U.S. intelligence officials.

"Since the early 1970s, the Soviets and their surrogates have increasingly used their national intelligence services to acquire Western civilian technologies," former CIA deputy director Bobby R. Inman told a Senate panel.

The Soviets' quest for technology begins with government publications, and visits to colloquia and trade fairs (Veremy had visited Software's booth at two trade fairs before he came to the Reston office).

If attempts to obtain a company's secrets through disgruntled or money-hungry employes fail, the Soviets have tried to order the product and have it shipped to a front company overseas. In addition, U.S. officials say, the Soviets and their East bloc allies have set up about 400 firms in the West, about 20 of them in the U.S., to export high-tech products to the Soviet Union.

To monitor and restrict the flow of U.S. technology to the Soviet Union, the U.S. government has taken several steps in recent years:

* Last January, the Defense Department's Defense Technical Information Center made it more difficult to obtain its bulletin detailing over 30,000 technical reports each year. The bulletin is now classifed "confidential."

* The Department of Commerce has restricted availability of newsletters published by the National Technical Information Service that list nearly 80,000 technical reports annually and provide information about U.S. government research and development projects. NTIS director Joseph Caponio concedes that the restriction only delays Soviet access, rather than prohibiting it.

* In January 1982, the FBI began briefing all defense contractors' employes, rather than just those with top secret clearances, on Soviet espionage tactics.

* An interagency Technology Transfer Intelligence Committee was established in early 1982 to coordinate intelligence efforts in the technological field.

* In 1982, the U.S. and its Western allies made a confidential agreement to tighten up on technology transfer to the Eastern Bloc. Lawrence Brady, assistant commerce secretary for trade administration, says this new awareness resulted in recent expulsions of Soviet diplomats from Western countries.

* The Department of Commerce, under frequent attack for lax enforcement of export regulations, increased from 30 to 100 the number of persons who monitor exports, and has set up a West Coast enforcement office to oversee exports from the Silicon Valley in California. Since July 1982, Commerce has referred 25 cases to the Department of Justice for possible prosecution, up from eight in the same period the year before.

Despite the restrictions the Soviets do not give up easily. Maguire said four Soviets were arrested recently in West Germany after trying to get access to the "Source" through an employe of a Software subsidiary there.

"They sure are persistent," said Maguire.