LONDON--German broadcasts said tonight the British Eighth Army had launched its long-awaited offensive against a broad front of the Mareth Line and implled that German and Italian troops had given ground at some points in heavy fighting.

Allied dispatches did not confirm the German reports but left no doubt that the all-out battle to drive the Axis African armies into the sea was at hand.

The Eighth Army struck along a broad front at 10:30 o'clock Tuesday night following a day-long artillery bombardment that swelled to a terrific barrage just before the attack, the German radio said.