The Federal Aviation Administration is under increasing pressure to speed restoration of the air traffic control system although the veterans who have kept it running since the massive controllers' strike in August, 1981, are tiring and replacements are not yet experienced.

Senior controllers and FAA middle managers expressed concern in interviews that, from a safety point of view, they will be asked to do too much, too soon, perhaps resulting in tragic mistakes as they transmit instructions to pilots and scan radar screens for a mind-boggling 85,000 flights each day.

They sense that, as the economy improves, more Americans will want to fly. That means airlines and business and pleasure aviation interests are increasing pressure on the FAA to further relax or even eliminate flight restrictions imposed immediately after the strike to keep traffic moving, although at a reduced level. Early reports this year indicate that air traffic is beginning to rebound after a two-year slump, and the FAA has promised to lift most restrictions by Dec. 31.

In interviews about the status of air traffic control 22 months after President Reagan fired 11,400 striking controllers, aviation safety specialists, airline executives, pilots, controllers and FAA officials told of a system performing safely, despite some disquieting incidents. They made these points:

* The central safety question is whether beginning controllers are being pushed too fast. FAA Administrator J. Lynn Helms insists they are not, while National Transportation Safety Board Chairman Jim Burnett worries aloud that they are. At a recent board meeting he said, "I sense . . . that we have probably moved too far, too fast, in removing controls on the traffic in the air traffic system."

In a major study issued May 19, the board's recommendations included one that the FAA "postpone planned increases in air traffic volume and services . . . until sufficient controllers are trained and qualified." Five days later, last Tuesday, the FAA reiterated the earlier message to airlines: almost all restrictions will be lifted by Dec. 31.

* Since the strike, no major accident has been attributed to controllers, but last year airliners were involved in 96 near-collisions, of which 13 were classified as critical by the FAA. A year earlier, 20 of 102 incidents involving airliners were called critical.

Two recent near-collisions in the Chicago area were apparently caused by controller errors and are under investigation. As shocking as these figures seem, they reflect improvement over the 1970s, when there were more controllers and fewer restrictions.

* Since the strike began, the airline industry has quietly endured flight and schedule quotas imposed by the FAA to ease demands on controllers who remained after the strike. Those quotas have been relaxed substantially, but FAA supervisors and middle managers have learned that controlling air traffic is easier and requires fewer people "if the peaks are flattened and the valleys filled," as one put it.

Airlines, on the other hand, feel that to compete they must be permitted to "peak," or schedule many airplanes in the same city at about the same time so passengers can make multiple connections. The fewer flights permitted airlines, the more businesses and residents in smaller cities will suffer from less convenient and less frequent service because airlines take care of New York, Chicago and Washington before they worry about Wichita or Charleston.

* Although Helms says most restrictions will be removed by the end of this year, significant glitches will remain indefinitely at four major airports: New York's La Guardia, Chicago's O'Hare, Denver's Stapleton and Los Angeles International. Until traffic at those airports returns to normal--and FAA officials from Helms down do not predict dates--commercial service throughout the nation will be affected to some degree.

A higher percentage of controllers struck facilities feeding La Guardia and O'Hare than at other locations, and the FAA has always had trouble recruiting qualified controllers to live in those areas. Construction projects are blocking full service at Denver and Los Angeles.

* More than 1,100 senior controllers or supervisors working traffic, or about one-sixth of the total of radar-qualified persons needed for a fully functioning system, are eligible to retire. And, 400 more will be eligible by the end of the 1985.

Such persons not only handle traffic but also do most of the training of new controllers, so they have the FAA stymied. A pay increase passed by the last Congress doubtless forestalled many retirements, and senior FAA officials believe the problem has eased. But other aviation interests are not as certain.

* Despite a major FAA effort to improve the volatile labor-management situation that led to the strike by the Professional Air Traffic Controllers Organization (PATCO), much must be done before there are effective results in the field.

Several senior controllers who did not strike describe their jobs today in the same angry terms as in the mid-1970s, when PATCO unrest was building. They say the FAA does not understand their problems and working conditions and uses dictatorial, uncaring supervisory tactics. There is also a new complaint: senior controllers are tired of spending at least half of their time training beginners because such work is more taxing than non-training duties. Crowding vs. Flying Rights

The air traffic control system is a complex network of telephone, radio and radar links among 20 regional air traffic centers, 238 sub-regional centers and 496 airport towers. Controllers across the country handle traffic in 550 different airspace sectors.

"In my sector, it's a struggle every day," said a controller in the regional center at Leesburg, Va. "We're not seeing the light at the end of the tunnel." A New York controller said his colleagues represent two extremes, "older fellows like myself and all new people. If the old-timers" retire, he said, FAA officials "will find themselves with problems."

Transportation Secretary Elizabeth Hanford Dole and Helms have told Congress that controllers are capable of handling as many flights daily as when the strike began. But the system cannot handle those flights over the same routes or at the same times as before the strike. Of necessity, traffic flow has been metered and rerouted to keep the pressure off green or overmatched controllers.

Helms noted in a recent speech that some current "fully qualified" controllers have never seen two six-plane stacks in a holding pattern over Lake Michigan while waiting to land at O'Hare. Such situations are not permitted to happen.

Stacking occurred regularly before the strike in a traffic concept called "free flow," under which controllers had to accept anyone who wanted to fly at any time. Since the strike, Helms has kept the system going by limiting flow. That means the government has interfered with the right to fly, a controversial point with the industry and business and pleasure pilots.

While such "flow control" restrictions may rankle, they have been accompanied by fewer near-collision reports. A near-collision is known technically as an "operational error" and, while many are not truly dangerous, all indicate that planes flew too close to each other.

The safety board, in its May 19 report, said the statistics essentially are meaningless, because many operational errors are not being reported or investigated.

Helms takes no comfort in statistical improvement. "I'm not sure we're getting them all," he said in an interview. "That's my concern. I don't mean to imply that people are purposely trying to hide them . . . . Are they too busy to report them? Or have they gotten to the point they don't really consider that significant anymore?"

Asked if the FAA has been lucky that no major accidents have been attributable to air traffic control since the strike, he said, " . . . Absolutely not. We've trained hard. We've used professional standards. And we have insisted on following procedures.I personally don't think there's luck atall . . . ." Parceling Out Airspace

Several airline pilots said controllers seem more polite and generally more professional and give them more direct routings. "It's smoother than ever," Pan Am Capt. Bob Sperry said. "We just don't get much trouble."

Thirty-five percent of experienced controllers who answered a recent safety board poll said the system is not as safe as a year before the strike.

The safety question is also a powerful argument in the economic issue of how much freedom airlines and other air traffic users should have in determining how often and where they fly. Not only are competing airlines involved, but also business and pleasure aviation, whose pilots often want to use the same airports as commercial airlines. As far as impact on the system, a Learjet carrying four corporate executives is no different than a Boeing 747 carrying 400 vacationers.

Dole said she has heard little grumbling from the industry or other users about access to the system. "I think generally there seems to be feeling we're on the right time frame" in removing restrictions, she said. Nonetheless, FAA officials in various centers and airport towers regularly hear from airlines seeking relief from flow control and other restrictions.

Under flow control, gaps between planes in flight were widened--in early days after the strike from 5 miles to 50 miles--and planes were held on the ground until they could be guaranteed trips to their destinations with no holding patterns.

In Jacksonville is an FAA computer, soon to be replaced by an even bigger one here, that oversees all flights nationwide and helps "flow controllers" decide when various air traffic sectors and airports will become saturated. Airline dispatchers check with flow controllers every day to find out what is in store.

Such limits have made the job much easier, especially for inexperienced controllers, and undeniably made the system safer. But a lot of airspace is not being used by airplanes at any one time.

So while Helms and other FAA officials seek to eliminate restrictions not forced by weather or runway capacity, they also talk about improving flow control computers, imposing holds before takeoff and other constraints.

Further, not one FAA manager interviewed beyond Washington thinks that flow control measures will or should disappear soon. Robert A. Frink, deputy manager of the O'Hare tower, said, "I don't really see getting away from some semblance of flow control for a long time. If we go back to free-run scheduling, where you get peaks of 46 or 47 flights in 15 minutes, you really get buried, the capacity of the system is exceeded . . . it gets expensive and frustrating."

An hour's drive away, at the regional center in Aurora, Ill., manager John Bacon said, "In three years, 80 percent of our controller work force will have been with us less than five years. We're training people in an environment where there are restrictions, not free flow. When it does go to free flow, will they have enough experience?"

The FAA intends to limit its controller staff to 14,000, compared with a prestrike level of 16,300. That is partly because some senior FAA officials believe that idle hands have time to create labor trouble. "We had all kinds of people sitting around twiddling their thumbs" before the strike, said Raymond J. Van Vuren, chief of the FAA's air traffic service. Heavy traffic demands at peak hours will be handled by supervisors and part-time controllers, Van Vuren and Helms said.

Airlines fear that flow control will become so ingrained that the institutional FAA--not the political one embodied in Helms--will find reasons not to expand.

Edwin I. Colodny, chairman and chief executive officer of Washington-based USAir, said in an interview, "I think the issue is: does the FAA intend to indirectly regulate the airlines" through flow control and other quotas after it is possible to remove flow control? "I am satisfied with my own conversations that as long as Lynn Helms is there, the FAA will not do that," he said.

Helms could not sound more in favor of free enterprise but is well aware that not everyone can take off from the same place at the same time. He has seen, he said, 27 specific requests for an 8 a.m. departure at La Guardia. "You couldn't do that even if you owned the airfield," he said. "But that's the airlines' business . . . . We ought to let them run their airlines, and let them do what they want to . . . ."

The airline business is changing as the control system is rebuilding, and the changes are putting more pressure on the system. With deregulation, airlines are scheduling as many flights as possible into one city at one time, just as Delta and Eastern have done for years in Atlanta. The so-called "hub and spoke" concept is "the most efficient way you can serve many communities," according to Joseph A. Lorenzo, Continental's vice president for marketing. "One flight can serve 30 destinations."

"From a competitive standpoint," Lorenzo said, "our hub in Houston is competing with American's in Dallas in trying to attract the same passengers." Thus, if the FAA eases quotas in Dallas but not in Houston, American gains and Continental suffers. Competitive Pressures -

Between 8:59 and 10:15 a.m. daily, Continental has 24 arrivals at Houston, and the same planes take off between 9:50 and 10:45, thus requiring 106 minutes for Continental's morning connections to clear Houston. Continental wants to do it in 80 minutes, which would mean additional strain on the air traffic system. The payoff for Continental is that travel agents searching their computers would see shorter connecting times and thus faster trips, one of the factors that such computers consider in displaying available flights.

"I don't think we're going to handle all of the demands of the air traffic control system the way the airlines and the others want it until, oh, mid-1984," Helms said. Later he amended that, saying, "By late '84, we ought to be pretty well able to handle demand . We will still keep flow control" to deal with weather or unexpected traffic jams.

Current holding-pattern restrictions will be relaxed so a few planes will be permitted to take advantage of gaps that might occur in the landing sequence, Van Vuren said, and every attempt will be made to let airlines and other users fly as often as they like.

Mandatory flow control, Helms said, is "not what a government agency should be doing. We should be creating capacity and safety and efficient use. Other than that, we ought to get the hell out of it. If you want to fly yourself into bankruptcy, that's your business . . . ."

On Long Island, where controllers at a subregional center sort out airplanes for Newark, La Guardia and John F. Kennedy airports, manager Charles Stafford said, "It really bothers me to hear airline marketing people say they want to go to a free-flow system. It's not realistic. I want my guys to bust their tails, but I can't see airplanes spinning around" in holding patterns.