MOSCOW (AP) _ The Soviet legislature on Monday ratified the treaty permitting German unification, formally ending the four World War II victors' authority.

''It's been 45 years since the war ended. It's time to live normally,'' said Marshal Sergei Akhromeyev, former chief of the Soviet general staff and an adviser to President Mikhail S. Gorbachev.

The agreement opens ''a new epoch of lasting peace and widescale cooperation between the Soviet and German peoples,'' according to a resolution that accompanied ratification. The other three victors - the United States, France and Britain - ratified the treaty last year.

The Supreme Soviet legislature also approved a Soviet-German nonaggression pact.

However, the legislature gave only general approval to two related treaties on the withdrawal of Soviet troops from German territory and on unspecified transitional measures, Tass said. The documents were sent back to committee to clarify details, the official Soviet news agency said.

Some legislators called for more housing for returning troops and more money from Germany, lawmaker Roy Medvedev told reporters. Germany has already agreed to pay $7.6 billion to the Soviet Union toward retraining demobilized troops and building new housing for them at home.

Medvedev noted this was the first time the two-year-old Soviet legislature had ratified a major treaty. He said many members did not understand they could not rewrite sections of a treaty worked out in bilateral negotiations in the same way they could tinker with draft domestic legislation.

The treaties, concluded by then-Foreign Minister Eduard A. Shevardnadze last year, symbolize the fall of the Soviet empire in Eastern Europe.

Lawmakers had predicted a stormy closed-door debate, but said during a break that the session proved to be far more tame.

Even Col. Nikolai Petrushenko, a hard-liner who said in a newspaper article Saturday that he would campaign against the treaties, said Monday he could be swayed.

''If my doubts are resolved, then I'm for it,'' he told reporters.

Petrushenko is a leader of the conservative Soyuz group of legislators, which pressed for Shevardnadze's resignation in December and wants Gorbachev to impose presidential rule in Soviet trouble spots or step down.

Petrushenko told reporters he was concerned with ''the return of cultural valuables stolen from us during the war,'' the interests of veterans who fought the Nazis, and the hundreds of dollars charged by the Germans to dispose of garbage from Soviet military installations.

The Soviet Union also apparently is concerned with a growing number of soldiers deserting from units stationed in the former East Germany.

More than 200 Soviets have fled, including 35 officers, 116 servicemen, 53 family members and 17 civilian employees, Maj. Gen. Vladimir Zhurbenko told Tass on Monday.

Soviet officials have repeatedly asked the German government to return the deserters for trial, to no avail, Zhurbenko complained.

German officials say deserting soldiers may request political asylum and must follow German law in processing these claims. So far no deserting Soviet soldier has been granted permanent asylum.

The six-nation ''Treaty on the Final Settlement with Respect to Germany,'' was signed in Moscow in September by the foreign ministers of East and West Germany, and of the four Allied powers.

The treaty, the climax of seven tough months of negotiations, put the seal of approval on unification that occurred Oct. 3. It scraps special Allied rights in Germany such as control of air corridors into Berlin.

Under the document, the Soviet Union lost East Germany as its most valued military ally. United Germany belongs to NATO.

The Soviets were allowed to keep their estimated 370,000 troops in East Germany for a maximum of four years, and Germany agreed to limit its united troop strength and renounce nuclear and chemical weapons.