The invention relates to a system for variable continuous distribution in four-cycle internal combustion engines. It is possible with this system to vary the extent and the opening and closing timing of the intake and exhaust valves. The invention is characterized in the independence of the valve opening and closing timing, and also in the independence of the intake and exhaust timing. According to the invention, the variable distribution system consists of a shaft receiving slidable retractable cams. The cams are inserted between a set of guide rails having variable positions and the valve lifters for the valves. The valve lift profile section will depend on the relative position of the guide rails. The variable positioning of the trains (and of the guide rails) relative to the camshaft and to the cylinder head is provided by a system of arms and pivots. A system of amplifying arms can be installed as an intermediate between the cams and the valve lifters to modify the extent of the opening.