Flexitime, the experimental program that lets many federal workers set their own hours and in some cases work a four-day week, is in trouble.

Congress ordered agencies to experiment with the set-your-own hours program several years ago. Idea was that it would cut down on tardiness, improve morale and expand service hours to the public.

Under flexitime, employes can--with the approval of supervisors--decide when they will come to work and when they will leave, provided they put in eight hours a day, or 40 hours a week. Most of the managers who supervise flexitime programs are not on it, either by choice or by orders of their agencies.

Backers of the flexitime program say it has done all it was supposed to do: Workers like it, offices can be manned for longer periods, and the problem of lateness is reduced because workers who come in late must make up the time before the close of the workday or be docked.

Many feds, especially people whose schedules allow them to work stretched-out days so they can take three-day weekends once or twice a month, have adjusted their lifestyles to flexitime.

Opponents of flexitime argue that while it is useful in some operations --where offices need to be manned over long periods--it is sometimes confusing and disruptive with the majority of the staff coming and going at different times.

Some managers complain that keeping track of people on flexitime schedules is a problem. Some say they often find themselves short-handed on Mondays and Fridays because of 4-day-week schedules. Others say that having people come in as early as 6 a.m. is pointless because most agencies, individuals or corporations they deal with do not start work until later. They also complain that some people who come in very early do not actually begin work until their boss, or other colleagues, arrive.

The experimental program on flexitime is due to end in March, unless Congress extends it.

On Wednesday, the House Subcommittee on Human Resources begins hearings on flexitime. Chairwoman Geraldine Ferraro (D-N.Y.) hopes to get hard numbers as to how many people are on it, how it is working and whether it is worth continuing.

The administration is expected to endorse extension of the flexitime experiment. But many officials and key managers have soured on the program and some agencies are expected to eliminate it, or reduce the number of people on flexitime, in the months ahead--unless Congress says otherwise.