KIEL, Germany, April 7 (Reuters) - It can cruise under water for weeks without surfacing, is virtually impossible for enemies to detect and is about to make the German Navy the most advanced non-nuclear submarine fleet in the world.

The first fuel cell-powered submarine began its maiden voyage on Monday after decades of development, weaving silently between passenger ferries and freight ships in the northern port of Kiel before heading out into the Baltic Sea.

Built at the 165-year-old Howaldtswerke Deutsche Werft (HDW) shipyard, birthplace of the modern submarine and the yard where Nazi Germany built the U-boats that terrorised Allied shipping in World War Two, the "U31" uses tanks of hydrogen and oxygen to feed fuel cells which convert gases into water and electricity.

The technology allows the submarine to prowl silently under water for two or three weeks without resurfacing -- a feat diesel-electric submarines cannot manage because they run on batteries when submerged and have to surface to recharge them.

As it generates no heat or noise from exhaust fumes it is also virtually undetectable, HDW claims, an asset the German Navy says will allow it to help allies set up underwater lines to protect ports or coastlines in hotspots around the world.

HDW is currently owned by U.S. investment group One Equity Partners but the technology is a key defence asset for Germany.

"For us it is a quantum leap," German Navy spokesman Gerhard Deisenroth told Reuters on board an HDW ship accompanying the U31's first sea trial.

"Now we have a boat that we can really use all over the world. If a crisis is brewing you can send a submarine to the area without being seen and without making a political statement."

The German Navy will put the first U31 into service next March, after its sonar systems have been deep-water tested and it has fired practice torpedoes in German and Norwegian waters.

Three more are on order and the Greek and Korean navies have also placed orders. But German government restrictions may limit the technology's export potential, with the current frosty political climate between Washington and Berlin creating a particular problem over sales to Taiwan.