By the time Signe Wetrogan takes her kids to school in the morning, her husband Leon has been at work for a couple of hours. And while she's still on the job late in the afternoon, her husband is already home, picking up the kids and car-pooling them to various after-school activities.

The Wetrogans, who live in Silver Spring, are both federal workers. They say they have coped with the dual stresses of employment and family life by taking advantage of "flexitime," an alternative work scheduling arrangement that allows them--within certain guidelines--to vary their on-the-job hours according to their personal needs.

"It takes away a lot of the guilt feelings you have but still lets us enjoy the advantages of a two-person income," said Mrs. Wetrogan, a mother of two elementary school-age children who works as a Census Bureau statistician.

Some 7.6 million Americans now participate in a form of flexitime, including employes at the American Security Bank and the D.C. Public Library. By far the greatest believer in flexitime has been the federal government, which in the past three years has established several types of variable work hour programs for more than 325,000 employes, including about 75,000 in the Washington area.

Now, however, the innovative scheduling procedures have come into conflict with the conservative management philosophies of the Reagan administration. Despite studies showing that most of the alternative work schedule programs have improved employe morale, stretched the hours of service to the public and eased commuter traffic jams and energy consumption, the government's experiment with flexitime may come to an end in two weeks.

Authorization for the three-year experiment expires March 29, and attempts in Congress to make it permanent have not gone anywhere because of the administration's desire to impose strict controls over the program, including a provision to require proof that an altered schedule improves productivity.

If some kind of compromise is not worked out, authorization for the government's 1,500 flexitime programs would expire, immediately shutting down some of them such as the four-day work week, and jeopardizing the rest.

The administration has strongly opposed any efforts to make flexitime permanent and has introducted its own legislation that would make major revisions in the program. Office of Personnel Management officials say they only want more management and productivity controls over current and future flexitime programs, but employe groups contend the additional restrictions the administration wants to impose would probably kill many of the government's flexitime arrangements.

"Happier employes make more productive employes, but they don't believe that," argues Linda Rothleder of the Federal Employed Women lobby. "Their whole theory is, 'We manage, you follow.' "

In the federal vocabulary, flexitime refers to several types of work schedules that allow employes to vary their starting and quitting times, the number of hours worked in a day and--with a compressed work week--the number of days worked in a week. Some federal agencies have long allowed employes to adjust starting and stopping times as long as they worked an 8-hour day, but in 1979 the Carter administration persuaded Congress to authorize a trial use of broader flexitime arrangements after reports that similar systems were working well in the private sector.

Testifying before a congressional committee earlier this month, Donald J. Devine, director of OPM, cited instances where flexitime did not work to the government's satisfaction. He said several agencies canceled the programs, particularly the four-day, 10-hour-a-day work week, after complaints of employe fatigue, lack of staff "coverage" for certain days or hours and declines in productivity and service to the public.

Devine said some flexitime experiments had meant "radical changes" in the times when employes reported to work and argued there was more at stake than employe morale. But when pressed by the committee chairman, he could not cite any examples where the government had been unable to terminate flexitime experiments that proved unsuccessful.

To supporters, alternative work schedules recognize the changing environment of the work force and the need for corporate management to adapt to those changes. In private industry, employers in fields as diverse as finance, trade, insurance, real estate and public administration have set up various types of flexitime programs for their workers. About a fifth of the federal work force and 42 state governments have experimented with variable working hours for employes.

"Flexitime is one personnel tool that gives a company or an agency the chance to have better morale for its workers, particularly in a time when people are wanting more control over meshing their personal and work lives," said Gail Rosenberg of the National Council for Alternative Work Patterns.

In its own study last fall OPM reported that the government's three-year experiment with flexitime had been generally well received, with 90 percent of the employes and 85 percent of the supervisers saying they wanted the programs continued. About 30 to 35 percent of the participants reported a small improvement in efficiency of operations; 50 to 60 percent said there had been no change; 10 percent reported small decreases in efficiency.

Additionally, employes said the use of variable working hours enabled them to perform their job requirements and still have time for outside interests. Workers used their days off or their free morning or afternoon hours to take part in family, church or other community activities, pursue educational interests or schedule personal appointments, such as visits to physicians or dentists.

Devine has since downplayed the OPM report, questioning its scientific methodology. He prefers, instead, to recall flexitime experiments at the Veterans Administration and the departments of Agriculture, Army and Air Force, where problems forced the termination of some variable work hour programs.

Devine and other administration officials say they want the sole right to decide when to start and when to halt such programs. The bill they have introduced in the Senate would give agency heads authority to begin flexitime programs, but only if they determine that flexitime would improve productivity and provide greater service to the public.

Rep. Geraldine Ferraro (D-N.Y.) has sponsored another bill that would permanently authorize the use of flexitime, provided both management and employe groups agree on the conditions. But so far, the House has failed to pass that measure, and the White House is lobbying against it.

Ferraro and other flexitime proponents have expressed concern that the administration bill would kill employe rights to bargain variable working hour proposals. And even those who favor stronger management controls have said the requirement that flexitime improve productivity is unduly restrictive.

Greg Lingafelter, who was in charge of alternative work scheduling at Agriculture and also participated in one of the experiments, concedes there were some problems and that managers were initially very skeptical about flexitime.

"But we've pretty well had positive experiences involving about 20,000 Agriculture employes," Lingafelter said. "About 25 percent of the managers still don't think there's adequate coverage of the duty tours, but my feeling is that they are not willing to take more time to manage and monitor."

With both sides far apart on a compromise, some current variable work hour programs may have to be abolished before the end of the month--a circumstance that Ferraro says could cost the government millions of dollars if it has to come up with overtime payments for employes who have worked 10-hour days but will now be denied the time off they have earned.

Sen. Ted Stevens (R-Alaska) has been trying to work out an agreement between employe groups and the administration, warning that time is about to run out on a program "which we all support." His office said yesterday that he hopes to have a compromise bill ready for introduction this week.

Caught in the middle of the dispute are federal workers such as Bonnie Wahlert, 28, an Agriculture Department employe who has scheduled her working hours in a way that gives her a day off every two weeks.

"It gives me another day at home with my little girl, who is 15 months old, and I can make personal appointments that I can't get on the weekends," said Wahlert, who lives in Manassas. "I would really miss that day off. There's so much I can get accomplished."