ANNAPOLIS -- Gov. William Donald Schaefer, whose fiscal reputation was built on spending money, now must find ways of saving it. Specifically, $150 million.

To avoid a looming deficit in the $11.5 billion budget, Schaefer two weeks ago ordered a freeze on state hiring and a cutback on vehicle purchases and out-of-state travel. He ruled out layoffs, a reduction in welfare benefits and, for now, a tax increase.

More specific proposals from his Cabinet secretaries will land on Schaefer's desk this week when the governor returns from a post-primary vacation in Ocean City. His decisions could determine everything from the number of students in university classrooms to the caseloads of welfare workers to the opening time of state parks.

Under instructions from the budget office, most of the projected deficit will be made up by trimming administrative spending in agencies that oversee health and welfare programs, universities, prisons and State Police. That much is known. But the administration is closely guarding details until the governor reviews and approves the plans.

"There were rumors that no troopers would be hired this year, and another version was that there would be layoffs," said Paul E. Schurick, the governor's press secretary. "Right now, I label everything as rumors. There have been no final decisions."

The budget problems are primarily due to the slowdown in the economy, which means tax collections are not as high as expected and more people need public assistance. It hasn't reduced tensions in Maryland any that the cuts come just as Virginia is trimming $1.4 billion from its two-year state budget, a retrenchment that will translate into layoffs of 1,100 state workers and higher college tuition in the Old Dominion.

Based on comparative budgets, Virginia's cuts are four times as deep as those contemplated in Maryland. But that hasn't allayed concern. "There is an insecurity being caused by the lack of answers right now," said a state official in Maryland.

Some broad outlines of Maryland's response to the downturn in the economy were emerging late last week.

University of Maryland officials said the number of classes could be cut and the number of students in remaining sections increased. Some classes may be dropped for a semester.

Chancellor Donald N. Langenberg also hinted that more drastic steps could lie ahead. "I think in circumstances like this we're forced to look at all forms of revenue enhancement," Langenberg said in an interview. "It means looking at the possibility of a tuition increase, a step-up in private giving, all kinds of things."

Langenberg said the university system is essentially "stalled" by cutting $39 million from its budget, wiping out the increase it got from the General Assembly this year as part of the campaign to bolster the university's academic standing.

The Department of Health and Mental Hygiene is expected to cut $43 million -- nearly half in the public health area -- from its $1.4 billion budget. Nearly $30 million will come from the Department of Public Safety and Correctional Services, where officials are considering delays in buying new vehicles, increasing the time troopers spend on highways and finding ways to increase the responsibilities of correctional officers in prisons.

At the Department of Human Resources, which oversees public assistance programs, administrators are looking for ways to save more than $22 million. But budget officials said there would be no cuts in General Public Assistance and Aid to Families with Dependent Children, the two major welfare programs.

Torrey C. Brown, secretary of the Department of Natural Resources, must cut nearly $3.5 million this year. "First, we're going to cut back on the purchase of vehicles and on travel," Brown said. "Last would be not renewing contracts or hiring."

Brown said the closing of some parks, or reducing park hours, is under consideration. "We haven't decided," Brown said. "It may not be as cost effective as some other things."

Schaefer, who came into office at a time of massive budget surpluses in Maryland, is best known for such high-profile projects as the Baltimore trolley line and the baseball stadium under construction near the Inner Harbor.

The surplus from the just-completed fiscal 1990 budget was $4.6 million, the smallest since the recession year of 1983. When he announced the projected deficit and ordered spending cutbacks, Schaefer emphasized that the shortfall amounted to only 1 percent of the state budget. However, the actual impact is closer to 5 percent, considering that federal aid and mandated programs such as public school aid are mainly beyond Schaefer's control.

"It's fair to say that essential services hopefully will not be affected," Schurick said last week.

Still, Schaefer apparently retains the support of legislators as he begins the first retrenchment of his term.

"It's a little tight, but $150 million is within the manageable range," said Sen. Laurence Levitan (D-Montgomery), chairman of the Budget and Taxation Committee. "Above that, we'd have serious problems."