DETROIT, NOV. 7 -- The scramble for Eastern Europe's emerging auto market intensified today as General Motors Corp. announced initial plans for its third car assembly plant in the region, this one in Czechoslovakia.

General Motors said the Czechs chose it above several competitors to negotiate for the conversion of an existing auto factory to assemble GM Opel cars for local sale and to manufacture 250,000 transmissions a year for export.

General Motors, which along with Ford Motor Co. has long had extensive auto manufacturing and sales operations in Western Europe, said it would be the first Western auto company to set up shop in Czechoslovakia.

But the operation with state-owned truck maker BAZ will be modest compared with an expected linkup between Volkswagen A.G. and Skoda, a Czech auto producer considered the best in Eastern Europe.

Germany's VW, Italy's Fiat SpA and GM lead the race to enter the Eastern European market, where cars are plagued with obsolete design and poor quality.

Fiat, which has done business with Soviet auto-making enterprises for decades, has predicted a doubling of the demand for cars in Eastern Europe -- to 5 million units annually -- by 1995.

That, analysts say, is particularly attractive as Western Europe rushes to eliminate trade barriers in 1992, opening up long-protected markets to at least some increased competition from Japanese auto companies.

Western automakers have entered into a variety of agreements with state-owned enterprises. They often overcome the lack of hard currency in Eastern Europe by agreeing to manufacture products for export on a dollar-for-dollar basis with materials they import.

Today, Fiat was reported to have promised $2 billion worth of investments in Poland's auto industry if the Poles agreed to prevent anyone else from building cars there.

Fiat proposed a 15-year plan to create several joint-venture companies in Poland that it would control.

Overall, Fiat is working on auto projects in Poland, Yugoslavia and the Soviet Union. They are valued at $8 billion, according to reports from Europe.

VW has the upper hand in what had been East Germany, where the market is expected to grow fastest.

GM said it is too early to put a price on its proposed Czech venture. A similar operation underway in Hungary is said to represent an investment of $150 million.