Horrendously poor telephone service provides a new market opportunity for express courier services in East Germany and much of Eastern Europe.

Both Federal Express Corp. and DHL Corp., competing carriers in the express mail business, plan to expand their service in East Germany. Federal Express is also expanding operations within West Germany.The company believes there is strong sales potential in East Germany. The inefficient telephone service is likely to make express courier services very popular as facsimile transmission of documents over telephone lines is next to impossible.

Unlike in the West, where facsimile service is believed to have cut into the growth of the overnight document business, the East lacks sufficient telephone lines. Those that exist generally are of poor quality.

Federal Express, which was slow to start in Europe - it introduced its service just six years ago - is making a strong bid at catching up with competitors. It will open a station in West Berlin on May 1 to serve both sides of the city. It plans eventually to open service stations in Leipzig, Dresden and Karl Marx Stadt.

The company entered the Soviet market on April 1, with service to Moscow, and began serving other major East European capitals, such as Warsaw, Prague, Budapest, Bucharest and Sofia in March. Federal Express also began flying to Belgrade and Zagreb in Yugoslavia last month.

United Parcel Service is also gearing up for the changes in Eastern Europe. The company began serving the Soviet Union,Hungary, Yugoslavia, Poland and East Germany last December.

The Soviet service is by a joint venture with Sovtransavto, the state- owned Soviet transportation company. UPS has a 50 percent stake, but company spokesman Ralf Schreckling would not reveal the size of the investment. The other Eastern countries are served by UPS' traditional brown trucks.

UPS has served only East Berlin so far, but beginning April 17, it will deliver to all East German cities. UPS says it can deliver letters and packages within 24 hours, assuming there are no holdups at the customs checks.

By comparison, DHL has long had a branch in West Berlin and has been active in major East European cities since 1983, when service to Yugoslavia began. Bulgaria, Hungary and Poland were added in 1984 and the Soviet Union in 1985. Czechoslovakia, Romania and East Germany came on board in 1986, according to company spokeswoman Ellen Maldaner-Muenst.

Within West Germany, Federal Express is also expanding domestic operations. Its courier service offers 24-hour package and freight delivery in 80 percent of the Federal Republic.

The company's 1988 purchase of Unilever's West German transport subsidiary Elbe Transport GmbH and its subsidiary, Kraftverkehr Klaus GmbH, gave Federal Express the base from which to offer the new service, said Peter Kellner, the company's Frankfurt sales director.

The company handles about 1,000 express packages nightly, operating out of a main hub in Frankfurt, with centers in Nurnberg and Wuppertal. It soon will open two more centers in West Germany.

At DHL, business between West Germany and East Germany for January and February increased by 50 percent from the same period in 1989. That has prompted company officials to consider expansion plans in Eastern Europe, but Ms. Maldaner-Muenst said there's nothing on the table right now.

DHL's document volume rose 12 percent in 1989, while the express business increased by 35 percent, for an overall increase of more than 20 percent.

The company's East European operation is based in Budapest, where DHL has a joint venture with the state-owned Hungarocamion, a truck company. DHL has invested more than $800,000 in its East European operation, most of it for computer and telecommunications facilities.

Lufthansa AG, the West German national airline, has no plans to expand its West-East German freight service right now. The carrier flies from several West German cities to points in East Germany, including Leipzig and Dresden.