Abstract: A rotary-block engine is provided with an eccentrically mounted cylinder block about the main drive shaft. The radial cylinders of the cylinder block each contain a reciprocating piston which is also eccentrically mounted about a secondary shaft, so that a point on the piston traces a path in the form of a hypotrochoid while a point on the cylinder block traces a path in the form of an epitrochoid. The secondary shafts are held in place relative to the main shaft by projections engaging in grooves of the side walls of the stationary housing, or alternatively by holders rotatably mounted about the main shaft.