West Germany authorities are investigating one of the country's largest arms exporters for shipping weapons to world trouble spots in violation of strict laws banning such sales.

The investigation by a special commission set up by the Federal Criminal Investigations Office and the Duesseldorf state prosecutor could have a significant implications for Bonn's sensitive policy governing the export of arms to non-NATO countries. The West German government tightly regulates the flow of weapons sold abroad, generally prohibiting arms sales to "areas of tension."

Tipped off that West German arms had found their way to the Middle East, South Africa and Argentina -- all clear tension zones -- authorities launched an examination of Rheinmetall, a machine construction and arms company based in Duesseldorf.

The company, which earned about $400 million in sales last year, has denied acting illegally, maintaining that it delivered arms only to approved countries.

At issue, however, is what happened after the legal sales. Federal authorities are concerned that the weapons may have been passed on or diverted illegally to third parties.

Neither company officials nor investigators will comment on the details of the inquiry, but West German sources have disclosed at least three trades that are being questioned.

Machine guns sold to Italy are said to have been shipped on to Saudi Arabia. An Italian ship captain allegedly switched the goods from one ship to another one night in the Mediterreanean.

Ammunition manufacturing equipment sold to Paraquay ended up in South Africa, after being diverted in a Brazilian port.

Light guns sent to Spain were moved on to Argentina.

West German trade law contains a so-called "final use" clause, which is supposed to prevent such transfers. It requires most importing countries to guarantee that arms bought from West Germany will remain in the country to which they are sold.

The clause is difficult to enforce, however, as Bonn officials readily admit. Economics Minister Count Otto Lambsdorff conceded this week that West German arms export controls are "not always watertight."

Conceivably, too, a German arms dealer may not know where others may be funneling weapons. This raises the question of whether West German companies should then be held responsible when arms they sell end up in the hands of off-limits users, although federal authorities suspect that arms merchants often have at least a strong hunch about the final destination of the weapons they sell.

The Rheinmetall case is likely to be used as political ammunition by the governing Social Democrat and Free Democrat parties, which have sought tighter controls over West German arms exports. Karsten Voight, a Social Democrat and member of the Bundestag, yesterday repeated demands for stricter parliamentary control of West German arms sales. In an interview published in the weekly Die Ziet, Voight criticized Bonn arms export licensing criteria as being "not very clear" and called on the government to issue a complete accounting of the nation's weapons export business.

Voight also cited coproduction arrangements as a means used by West German armament manufacturers to skirt Bonn's export controls. Under such contracts, weapons based on West German patents can be licensed for production by companies in France, Switzerland, Italy, Spain or elsewhere, and are then subject not to Bonn's export laws but to the often more lax controls of the country in which the arms are made.

The West German government, while sensitive to the pressures building in the wings, has tried to balance the demands for arms regulation against the economic health of a domestic arms industry that earned about $860 million in exports last year.

Moreover, Bonn sought this year to boost the country's sinking shipping industry by successfully pressuring Western allies to life postwar restrictions on the size of German-built warships, previously set at 3,000 tons for surface vessels and 1,800 tons for submarines. While the West German Navy has no current need for larger ships, the move was intended to free shipyards to accept large orders from abroad.