Needy families in Washington's wealthy suburbs had better luck getting federal money to help pay their home heating bills last winter than families from the area's poorer neighborhoods, according to recently released figures from six local poverty agencies.

More than one-fourth of the federal grants for emergency heating aid distributed in the metropolitan area went to Montgomery County, where fewer than one-tenth of the area's poor families live.

By contrast, families in the District received less than half the emergency heating aid given out locally, although the city houses two-thirds of the area's poor, according to government statistics.And nearly one-third of the aid the District did receive remained unspent.

Congress is now wrestling with the final details of this winter's program, which is designed to avoid some of the problems encountered last year.

In one major change, the amount of aid will increase eightfold this year to $1.6 billion.

Like last year, the program will berestricted to low-income families -- an urban family of four can earn no more than $8,375 to qualify for emergency aid, up from $7,750 last year.

Unlike last year, applicants will not be required to present a notice from their fuel dealer showing that their fuel supply has been cut off because their bills hadn't been paid.

Last Year, $592,693 of the $200 million national fuel aid program was spent in the Washington area to help pay the heating bills of 3,368 families.

However, the distribution of that aid locally reflected the varying administrative skills of the local poverty agencies as much as the needs of the people they serve.

Take for example, the experience of Montogomery and Prince George's counties. Both Maryland subdivisions received their money from the state Department of Human Resources, which planned to give funds to local jurisdictions on the basis of need.

Prince George's had nearly twice as many needy families as Montgomery in 1970; more recent figures indicate this gap has widened.

Yet $92,797 in federal aid was given out to 560 families in Prince George's, while 800 households in Montgomery County received $159,246 in aid, both as direct payments to fuel dealers and as food vouchers for families who had spent as much to keep warm that they had little left to buy food.

"We did the best we could," said James Foley, who heads the Prince George's Commission on Aging, which was assigned to run the emergency fuel aid program.

Explaining the distribution of the funds, Frank Welsh, of the Maryland Department of Human Resources, said, "In earlier years we gave Prince George's more money and they didn't need it."

Last winter, "I held back money in the state here in cast some programs did better, ran out, and needed more . . . I held back on funds from several agencies, one of them being Prince George's County," Welsh continued.

"We're serving the state. You have to put it in perspective. You can't tie up money if it's not going to be used."

Welsh's strategy was borne out by the results. Of the $130,559 sent to Prince George's under the two emergency programs, 14 percent was returned unused.

The Montgomery County Community Action Agency, meanwhile, used up it original grant and came back for more, receiving a total of $180,474 from the state and returning only 7 percent.

The allocation of Northern Virginia's fuel aid paralleded the areas of need more closely, although Arlington County's community action agency was able to reach only 61 families and was forced to return $20,531 nearly twice as much money as it distributed.

Some 230 families in Fairfax received the benefit of $39,928 in aid while $27,459 was spent to help 179 families in Alexandria. $"Remember, they (the poverty agencies) only had about a month to distribute the money," said Joan Williams, an official of the Virginia Association of Community Action Agencies. "There was just wasn't very much time."

Because of what some local officials said were administrative delays in the federal government, some local agencies had only from last May 15 to last June 30 -- well after the heating season -- to identify needy families and send money to their fuel dealers.

District officials also complained of the rigid federal timetable for spending the money.

The community services division of the United Planning Organization managed to reach 1,500 families with $262,795 in aid.

Nonetheless, UPO officials concede that many families were left out -- thanks, they say, to the rules of the program. "We do have a huge renter population," said Lillian Durham, who heads UPO's community services division.

Ed Freel, a federal Community Services Administration official who ran the heating aid rpogram in Delaware lasat year and who heads this year's program nationally, said that the old rules did force poverty agencies to cope withmore than they could handle.

"In some cases we'd have people calling the local utilities or heating oil suppliers and begging them to send their customers cutoff notices," he said.

Under this program, local poverty agencies will have three more months, until Sept. 30, to make payments to fuel dealers, and state governments will have more authoritiy to determine how to spend the money.

In the final charge, the amount of aid will increase to $1.6 billion to be distributed under three programs. The federal Community Services Administration is already getting ready to distribute $250 million of that money to help families with heating emergencies. And Congress is about to approve the additional $1.35 billion in aid.

The only remaining arguments on Capitol Hill concern the formula that will be used to parcel out the money among the states. But last year's experience in the Washington area indicates such formulas often bear little relation to the final distribution of aid.

Although Freel of the federal Community Services Administration is optimisic about this year's program, there is still concern in other quarters.

While the states have more flexibility and more time to run their programs this year, "the states still don't know how much money they'll have," said Scott Bunton, Community and Human Resources Director for the National Governors' Conference.

"That means less than a month's lead time for planning. That's no way to run a boat."

The problems that plagued the program last year "are mostly a reflection of the fact that it's very hard for a large government to act rapidly in a complex situation that involves many different state and local contact points," said Robert D. Reischauer, and assistant director of the Congressional Budget Office.

"You're designing a seasonal program, not like food stamps or welfare, so you're not going to employe people who are specialized in this," he said.

"That programs like this work tolerably at all is a minor miracle," he added.