Latin America's last military strongmen - Noriega of Panama, Pinochet of Chile, Stroessner of Paraguay - are openly defying the United States, once a power that could make or break Latin governments with ease.

Washington takes credit for having encouraged the democratic wave that swept Latin America since 1979, when Ecuador became the first of 10 countries to switch from military rule to democracy.But the United States has been unable to drive from power Latin America's remaining generals: Panama's Manuel Antonio Noriega, Chile's Augusto Pinochet, and Paraguay's Alfredo Stroessner.

"The dictators are thumbing their noses at Washington as if to show that the days of the big stick are over," said a Latin diplomat, referring to Theodore Roosevelt's remark that U.S. policymakers should "walk softly and carry a big stick."

These days, Americans tend to walk noisily but carry a small stick, say critics of the Reagan administration. During more than seven years of Reagan's presidency, U.S. prestige in Latin America has declined.

Panama is a case in point, analysts say. Few countries have been tied to the United States as closely as Panama, where more than 10,000 U.S. troops are stationed along the banks of the strategic U.S.-run Panama canal.

American influence is evident from McDonald's hamburger stands to television soap operas. Through much of its history, Panama was run from the U.S. Embassy as much as from the presidential palace.

But for all its close ties and long dominance, the United States has been powerless to dislodge Noriega, a 50-year-old career officer who was treated as a trusted ally before Washington began siding with his domestic opponents a year ago.

Since then, Noriega has weathered figurehead President Eric Arturo Delvalle's attempt to unseat him as armed forces chief - which ended with the ouster of Delvalle. A few weeks later, Noriega survived a coup attempt and crushed his army opponents. Diplomats say both efforts had U.S. encouragement.

A U.S.-engineered cash crisis wrecked the service-based Panamanian economy, but neither that nor a cut-off of U.S. aid budged the defiant general. Noriega also shrugged off a U.S. indictment on charges of having turned Panama into a conduit for Colombian cocaine.

And Noriega made a mockery of statements by senior Washington officials such as Assistant Secretary of State Elliott Abrams, who in March reported that the general was hanging on "by his fingertips."