WASHINGTON (AP) _ George Bush and Michael Dukakis each promise to cut the federal deficit if elected president, but their proposals for new programs could put the United States deeper in debt, economic and political analysts say.

Each candidate has described or endorsed plans covering areas from defense to child care that could total billions of dollars in increased spending if adopted by Congress without offsetting cuts in other spending.

''These guys are going in the opposite direction,'' said Professor James Thurber, director of the Center for Congressional and Presidential Studies at American University. ''They're talking about spending money rather than saving money.''

Henry J. Aaron, senior fellow in economic studies at the Brookings Institution, cited ''the failure of both candidates in my view to deal responsibly with the deficit problem.''

Bush and Dukakis have expressed concern about the budget deficit, which was $155 billion in fiscal 1988, which just ended. The national debt, under $1 trillion when Ronald Reagan took office, is now more than $2.6 trillion.

Concerns about the deficit's potential effect on the U.S. and global economies played a role in last year's drop in world stock markets and led to an agreement between Reagan and the Congress to limit spending.

Thurber said the U.S. budget deficit remains one of the main concerns to foreign investors, who now are loaning the money to pay for more than half of the debt and are concerned about the security of their funds.

''They don't have very many other places to send their money, but they're wondering if they'll ever get their money out of this situation,'' said Thurber.

Marvin Kosters of the American Enterprise Institute said new programs could be adopted without increasing the budget deficit if other programs are cut, but ''not painlessly, and not without political conflict, certainly.''

Aaron said he thinks pressures in Congress will keep any new programs small and have them ''self-financed'' by eliminating tax benefits or cutting other programs.

Dukakis has said he would cut some nuclear weapons, but his pledge to build up conventional arms could prove ''very costly,'' said Thurber.

Bush has criticized Dukakis for opposing both the mobile MX and Midgetman missiles, but acknowledges he cannot afford to press ahead with both. Bush says Dukakis is naive to let the Soviets know in advance what missiles he will eliminate.

Bush's proposals include a $3.7 billion ''Invest In Our Children'' package aimed at children of low-income families that would help provide day care, more pre-school education and better health care.

Dukakis endorsed the concept, but not the exact dollar amount, of the $2.5 billion ''A Better Child'' day care bill that failed to win approval in Congress this year. It would set federal standards and funnel money to states to expand day-care slots.

Dukakis wants to spend $100 million on prenatal health care that he claims would pay for itself in a year because infants born under the plan would be healthier and require less hospital care after birth.

Dukakis also wants to require all but the smallest employers to offer basic health insurance to workers and their families - a move he says will cost the government nothing, but which Bush says amounts to a new tax of at least $35 billion on those businesses. Dukakis says his plan would insure 22 million of the nation's 37 million uninsured.

Aaron said that over time it would reduce tax revenues because it would shift some income from the taxable category to the untaxable fringe-benefit category.

Bush proposes a reduction in capital gains taxes, which would benefit people with investments in the stock market and elsewhere, at a cost estimated by the Congressional Budget Office at $3.9 billion a year.

Bush claims the tax reduction would free up money for more private investment, creating jobs and stimulating the economy; thus, in the end it would work toward reducing the deficit, because the government would have more people paying taxes.

Bush vows he would adopt ''no new taxes'' and claims he would eliminate the deficit by putting a ''flexible freeze'' on government spending to keep total growth at the inflation rate.

Dukakis says he would increase enforcement of tax collection and would raise taxes only as a last resort. But ''they're just not going to get that much more money out of it,'' said Thurber, adding that the Reagan administration has already increased the number of agents pursuing tax cheats.