An internal combustion piston engine comprising at least one cylinder head, said cylinder head closing at least one cylinder, inlet and outlet channels of said cylinder head being regulated, each one, by at least one inlet and outlet valve that is loaded by a closing spring, said inlet and outlet valves being activated by roller tappets (1) driven by cams of a camshaft and, if appropriate, by further transmission elements, said roller tappets (1) comprising at ends oriented away from rollers (7) of the roller tappets, two flattened portions (2) that are arranged substantially parallel to each other while being operatively connected to two matching inner surfaces (9) of an anti-rotation bridge (10) made typically of plastic, a spacing dimension of said flattened portions (2) at least partially overlapping a distance between said inner surfaces (9) and, starting from a mounting position of the roller tappet (1) in the anti-rotation bridge (10), an adjustment between the flattened portions. (2) of the roller tappets (1) and the inner surfaces (9) of the anti-rotation bridge (10) is varied with a tendency to adjustment with lash in direction of an operating position of the roller tappet (1).