The United States is rapidly increasing its military ties with nations large and small, thanks to the war on terrorism.

That means more U.S. soldiers will be spread around the globe in coming years, despite President Bush's warning during his election campaign that the military was stretched thin, with too many overseas deployments.

Already, American special forces train armies across Africa. The Pentagon fights war games in the Middle East. U.S. soldiers engage in scores of joint training exercises from South America to Southeast Asia.

Even before Sept. 11, the military had a presence in 140 countries worldwide.

Now it is busy expanding — or considering expansion — not just in Afghanistan, where the war against accused terror mastermind Usama bin Laden is taking place, and neighboring Uzbekistan and Kyrgyzstan, but in a slew of countries beyond: Armenia and Azerbaijan in Central Asia to Somalia in East Africa to the Philippines and Indonesia in Southwest Asia.

``Overall, the American military global presence is more pervasive today than at any point in American history,'' said John Pike, a military analyst in Washington.

Defense Secretary Donald H. Rumsfeld has suggested a pullback in only one place — a cut of about one-third in NATO troops on peacekeeping duty in Bosnia.

The new reach of America's military is worrying some nations.

Iran is increasingly nervous about being encircled by countries with new U.S. military ties, said Judith Kipper, a Middle East expert in Washington. China has long worried about American power. The military presence worldwide also could further anger Islamic hard-liners across southwest Asia and the Middle East.

Bin Laden first targeted America when thousands of U.S. troops who came to Saudi Arabia to fight the Persian Gulf War stayed on to maintain regional security.

During his 2000 campaign for president, Bush criticized his opponent, Al Gore, and the vice president's boss, President Clinton, for overextending U.S. military forces by intervening in places where vital U.S. security interests were not at stake.

Yet a recent Pentagon paper identifies vital American security interests in almost every part of the globe, with the notable exception of Africa.

The Afghan campaign again has taught U.S. officials that it pays to have relationships with countries important and obscure worldwide, whom the United States may need tomorrow, national security adviser Condoleezza Rice said recently.

After the Sept. 11 attacks, the United States moved quickly to strengthen ties with Pakistan so it could use Pakistani air bases. It approached the former Soviet republics of Uzbekistan and Kyrgyzstan and reached deals to put air bases in both.

In return, those countries get valuable help with military training or access to equipment. Countries like Singapore, where Navy ships dock, get a public linkage with America that might deter aggression, even if the United States makes no formal guarantee of military help.

The United States also increasingly tries to preposition military equipment worldwide, to lessen its dependence on cargo planes when trouble pops up, said Loren Thompson, an analyst at the Lexington Institute in Washington. A recent Pentagon study proposed putting even more equipment in the Arabian Sea and Indian Ocean.

``Coming out of Desert Storm (in 1991), we started to build up prepositioned things,'' Pentagon spokesman Rear Adm. John Stufflebeem said Monday.

In some cases, as it courts a country's military forces, the United States is willing to set aside human rights or other problems.

U.S. officials want to help Indonesia fight possible member clusters of bin Laden's al-Qaida network, for example, but are under restrictions because of human rights abuses there, Deputy Defense Secretary Paul Wolfowitz recently told The New York Times. Those restrictions ``really need to be reviewed in the light of Sept. 11,'' he said.

The United States doesn't trumpet much of the military cooperation. Uzbekistan, for example, is skittish that its role could anger Islamic hard-liners and thus has pressed U.S. officials to restrict news coverage. Rumsfeld and his spokeswoman, Victoria Clarke, have said that is a fair deal, in return for base access.

Saudi Arabia also doesn't talk about the thousands of U.S. forces there. That trend will only grow as America's presence grows, analyst Pike said.

In both the Persian Gulf and central Asia, he said, ``A great deal is being done to downplay the thing.''