A rotary-piston internal-combustion engine comprises a rotating block with three radially situated cylinders with pistons and an outside placed stationary case with two intake ports and two exhaust ports. Between the rotating block and the stationary case there are sealing parts and connecting rods, connected to one crank pin of a crankshaft. Between the crankshaft and the rotating block there is gearing for three times higher revolutions of the crankshaft in the opposite direction with respect to the rotating block. In the stationary case there are at least two spark plugs placed on the opposite sides. The bore of cylinders is 2 to 3.5 times higher than the stroke of pistons and all sealing parts with pressure springs that seal spaces of cylinders to the outer stationary case are placed in cavities in the stationary case.