PRAGUE, Czechoslovakia (AP) _ Ten U.S. inspectors on Friday completed the first inspection of a former base for Soviet nuclear missiles in this Warsaw Pact country, the official CTK news agency said.

The inspectors arrived Thursday after permission was granted for the inspection at the central Czechoslovak town of Hranice, 180 miles southeast of Prague, in accordance with the treaty eliminating U.S. and Soviet intermediate-range missiles.

After signing a report on the on-site inspection of the ''combat positions and other equipment'' used by units of the Soviet army until spring, the group left ''with a Soviet and Czechoslovak escort for Prague,'' the report said.

A second group of U.S. missile experts arrived in East Germany Friday to inspect sites covered by the superpower treaty, the state-run ADN news agency reported in Berlin.

ADN said the Americans were greeted at Leipzig airport by East German and Soviet officials. It did not say where they were going or give any further details.

Twenty other U.S. missile experts arrived in East Germany Monday to inspect sites. They left Wednesday.

In Czechoslovakia, Soviet troops stationed with the SS-12 short-range missiles began pulling the weapons out in February, even before the U.S. Congress ratified the treaty signed last Dec. 8 by President Reagan and Soviet leader Mikhail S. Gorbachev.

CTK said Thursday the 39 missiles with a range of 300 to 600 miles and 24 mobile launchers were withdrawn from Hranice in February and March.

The base now houses a Czechoslovak army unit, CTK said.

Col. Lawrence Kelly, identified by CTK as head of the American inspection team, was quoted as telling the news agency ''all four former action stations, including all parts constituting one installation covered by the agreement, were checked.''

Kelly reportedly praised the inspection as a step to strengthen mutual confidence and understanding, CTK said.

Under the agreements signed by the United States, the Soviet Union, Czechoslovakia and East Germany, the inspection can take 24 hours and may be extended by another eight hours, the agency said.