American forces are hunting terrorists in Afghanistan, dispensing advice in the Philippines and pondering counterterror programs in Yemen, Indonesia, Georgia and beyond.

What country is next? And where will it end?

"So long as there's Al Qaeda anywhere, we will help the host countries root them out," President Bush said Wednesday.

There probably will not be one place tackled next, but rather a number of them, said Gen. Tommy Franks, commander of the war in Afghanistan.

Franks said he expects to recommend that the U.S. military help train Yemeni forces to pursue Al Qaeda and other terrorists. Simultaneous battles against terrorists are likely at various places around the globe, with different approaches tailored to different nations, he told a House committee.

"We will not use the Afghanistan model" everywhere, he said.

Cells of Usama bin Laden's terror network are believed operating in 50 to 60 countries, officials have said, and the prospect of widespread post-Afghanistan military expansion drew a warning on Capitol Hill.

"If we expect to kill every terrorist in the world, that's going to keep us going beyond doomsday," said Sen. Robert C. Byrd, D-W.Va., chairman of the Senate Appropriations Committee.

Byrd was speaking of Pentagon discussions about sending as many as 200 Americans to help train the military in Georgia, a former republic of the defunct Soviet Union, amid sketchy reports terrorists have taken refuge in the Pankisi Gorge near Georgia's border with Russia's breakaway region of Chechnya.

It would follow deployment already this month of 160 special forces to the Philippines to train local forces fighting terrorists.

The Pentagon's intentions in Georgia are not strictly a counterterror campaign, Marine Gen. Peter Pace, vice chairman of the Joint Chiefs of Staff, told a Pentagon news conference.

Rather, he said, the goal is to help the Republic of Georgia gain sufficient military strength to defend itself, which would make it more secure and less in danger of attracting terrorist groups in the future.

Still, Georgia is just one example of the cooperation Bush wants with dozens of countries where Al Qaeda or other terrorist networks have toeholds. The United States blames Al Qaeda and its leader, bin Laden, for the Sept. 11 terror attacks.

In some regions, the U.S. military might provide training and other support to governments strong enough to handle anti-terrorism operations themselves. Elsewhere, U.S. troops may have to do some of the fighting themselves, as they have in Afghanistan.

In still other countries, U.S. military involvement in anti-terror efforts won't be explicitly related to Al Qaeda or other terrorist organizations whose global reach directly threatens the United States. The administration has provided machine guns, helicopters and military advisers to Colombia, for example, in its fight against anti-government terrorists, but there is no known Al Qaeda presence there.

In another approach, the Bush administration has authorized the construction of a radio transmitter to carry broadcasts from the Iraqi opposition to Iraq's Saddam Hussein, The New York Times reported in its Thursday editions.

The report quoted an unidentified State Department official as saying the administration had given tentative approval to the idea of building the transmitter in Kurdish Northern Iraq, which is protected by U.S. and British military overflights, or in neighboring Iran, if the Kurds or Iranians agree.

The Bush administration has not provided an exhaustive list of countries it believes have links to Al Qaeda or other terror networks, or have terrorists operating within their borders, but they are known to include Sudan, Indonesia, Malaysia, Iran and Iraq.

The timing, degree and manner of U.S. involvement around the world to root out terrorism in some cases will depend on regional sensitivities.

Georgia, which gained independence from the Soviet Union in 1991, has Russia to worry about; Russia considers the Caucasus region to be its sphere of influence and resents U.S. intrusion.

Yemen may be a similar case. The government there has pledged itself to help fight global terror but has not requested U.S. combat troops. It is interested, however, in military training and aid to create a maritime force to guard its 1,500-mile Arabian Peninsula coastline.

At least two Al Qaeda suspects wanted by the United States are believed hiding in Yemen. In October 2000, terrorists attacked a U.S. Navy ship in the Yemeni port of Aden and killed 17 American sailors.

Indonesia is another complicated case. U.S. officials believe Al Qaeda cells may be operating in Indonesia, and Washington has offered financial aid to train Indonesian police. The administration wants to resume military aid to Indonesia but is inhibited by a congressional ban imposed after the Indonesian army devastated East Timor in 1999.