Abstract: The invention relates to a coupling device comprising a sliding member sliding mounted on one driving shaft but adapted to slide axially thereon for varying the angular timing of another driven shaft in relation to said one driving shaft, notably in the case of a valve gear timing system of internal combustion engine. A bevel gear is rotatably mounted integral with said other shaft, at the adjacent end of said one shaft, a pair of bevel-toothed segments meshing with diametrally opposed sectors of said bevel gear and pivotally mounted to a diametral pin carried by said other shaft, each bevel toothed segment being rotatably solid with a lever formed with a fork-shaped cavity for receiving a driving pin carried by said sliding member, the cavities provided for said pair of segments being opposed to each other and formed on either side of said other shaft, whereby the translation of said sliding member is attended by opposite angular movements of said bevel-toothed segments.