They sit in small rooms monitoring telephone calls to Soviet bloc embassies; they tail cars with diplomatic license plates whose drivers are suspected of espionage, and -- occasionally -- they tap the telephones of American citizens who are believed to be selling the nation's secrets to foreign governments.

In the last week, they have arrested a naval intelligence analyst suspected of selling classified information to Israeli intelligence agents; a Central Intelligence Agency linguist who allegedly had been spying for China more than 30 years and a communications specialist at the top-secret National Security Agency accused of selling information about worldwide U.S. eavesdropping systems to the KGB, the Soviet secret intelligence service.

"They" are FBI counterintelligence agents, and the growing number of espionage arrests they have made over the last seven years -- culminating with a record 14 arrests so far in 1985 -- has propelled their work, their growing number -- more than 1,200 -- and the debate over how broad their powers should be, to the center of national attention.

"It looks to me like we need more prosecutions because there appears to be an unusual number of Americans spying against this country," said former attorney general Griffin B. Bell, who has been given credit for taking the first steps during the administration of President Jimmy Carter toward reversing a decade-long policy of not prosecuting U.S. citizens caught selling secrets to foreign governments.

But why have there been so many espionage arrests all of a sudden? Is more spying going on? Is the Federal Bureau of Investigation getting better? How great is the damage to national security?

Several officials said this week that it may take years and millions of dollars to complete the "damage assessment" from this year's spy cases alone. Most officials agree at the outset that such an assessment will conclude that U.S. intelligence has suffered "serious losses" in its agent networks abroad and in its ability to electronically eavesdrop in key areas of the world without fear of countermeasures designed to cut off these channels.

As for timing, a number of officials offered the view that the cases are largely coincidental in timing, and result from improved use of law enforcement tools and from increased awareness and vigilance by government employes who have access to classified information.

Officials have pointed to the arrest a week ago of Jonathan Jay Pollard, a naval intelligence analyst, as an example of greater security consciousness in the intelligence community. Pollard's coworkers reportedly turned him in after he requested some highly classified reports that were outside his area of responsibility.

Said Navy Secretary John F. Lehman Jr. in an interview, "It shows that we are now much more active in counterespionage and we're tightening up the system."

But officials said the best security measures do not always catch the spy.

Of the major cases this year, most have begun with a tip, these officials said: The Navy spy ring led by John A. Walker Jr. started with a telephone call from a disgruntled ex-wife; the cases of former CIA officer Edward L. Howard and NSA employe Ronald W. Pelton, both of whom have told the FBI they sold secrets to the Soviet Union, were developed by tips from Soviet KGB officer Vitaly Yurchenko, who sought political asylum in the United States in August and returned to Moscow early this month.

U.S. officials have not said how they detected the activities of Larry Wu-Tai Chin, a former analyst and linguist for the CIA's Foreign Broadcast Information Service (FBIS), alleged to have been selling classified information to Chinese intelligence since before the Korean war.

Of Chin's alleged spying, former CIA Director Stansfield Turner said in an interview "it's distressing" that the leak went on so long without being detected. Turner added that when a CIA employe travels to a foreign city such as Hong Kong -- where Chin is alleged to have passed secrets to Chinese agents -- "hopefully . . . we know from the CIA case officer there what he is doing and who he is seeing."

But Chin allegedly operated for years undetected, presumably undergoing periodic security checks while he went on providing information.

In the flurry of investigations, other conspicuous lapses in U.S. counterintelligence capabilities have surfaced.

For instance, in 1981 when a Titan nuclear missile officer from Kansas walked into the Soviet Embassy here to sell information, the FBI spotted him and overheard his telephone conversations with Soviet officials. But a year earlier, FBI agents failed to detect a visit to the same embassy by Pelton, the NSA ex-employe arrested early last Monday, who went there to sell what he knew about NSA intelligence programs targeted at the Soviet Union, according to an FBI affidavit.

Also, Pelton has told U.S. officials that on one trip to Vienna, he stayed at the residence of the Soviet ambassador, undetected by western intelligence forces that monitor Soviet espionage in Vienna.

So while the FBI has had an unusually productive year, the buildup in spy-hunting resources is "minor compared to the reason we are catching more spies," said Roy Godson, an intelligence expert and professor of government at Georgetown University. "But," he added, "the problem has begun to be addressed."

Between 1966 and 1975, there were no federal espionage prosecutions, according to a Congressional Research Service study. Since then, however, U.S. officials have made 49 cases against espionage suspects.

Former attorney general Bell said the swelling number of espionage cases involving Americans shows that "we went too long without using prosecution as a deterrent." Bell said the policy shift during the Carter administration was partially motivated by egregious intelligence losses, such as in the case of William P. Kampiles, a CIA employe who in early 1977 sold the "system technical manual" for the KH11 Keyhole series reconnaissance satellite to Soviet agents.

The debate over whether to prosecute Kampiles raged for weeks, Bell said in an interview, and was only resolved when Bell took his argument to President Carter, who decided in favor of prosecution.

"The intelligence community had come to believe that every time you prosecuted a spy, you would lose the secret, and that it was better public policy -- the best of two evils -- to let the spy go and keep the secret," Bell said. "But I had the idea that you could prosecute these cases without losing the secret."

Along with Bell's policy decisions came statutes and law enforcement procedures that FBI agents have utilized and which prosecutors will rely on in coming months to prosecute the current crop of espionage defendants. They include the Foreign Intelligence Surveillance Act and the Classified Information Procedures Act, the "anti-graymail" statute.

The Foreign Intelligence Surveillance Act set up a court of seven judges in Washington to review FBI requests for wiretap authority and the anti-graymail law set procedures in criminal spy trials for judges and juries to examine classified information outside the public view. One fear had been that spy defendants would use the threat of exposure -- graymail -- to win dismissal of charges.

The annual number of wiretap requests jumped from 319 to 549 between 1980 and 1983.

Reagan administration officials said this week that they have continued this "high priority" on espionage prosecutions and that the public should expect to see a greater number of cases.