A valve train for internal combustion engines utilizing an inverted bucket tappet with a pivot structure operatively disposed between the tappet and the end of the valve stem allowing the valves to be angulated with respect to each other and to the axis of the cylinder in both the transversal and the horizontal planes of the engine. Accordingly on a multi-valve engine, the valves extend radially from the associated combustion chamber to open and increase space in the center of the cylinder head for spark plugs, injectors, or pre-combustion chambers and so that the combustion chamber can be designed with a hemispherical surface, with tangentially disposed valve heads. The construction allows the use of large valves in conjunction with stronger, better-cooled valve seats and bridges. The tappets can be actuated conventionally by direct-acting overhead camshafts, or by rocker arms and "T" bridges.