Engaging device in a vehicle gear box

In an engaging device for a gear freely rotatably mounted on a shaft in a transmission, for locking the gear to the shaft or releasing the gear from the shaft, comprising an engaging sleeve mounted non-rotatable but axially displaceable relative to the shaft, and provided with engaging teeth, and a tooth rim adapted to be joined to the gear and provided with corresponding engaging teeth, said engaging teeth of the sleeve having pointed end portions and opposite flanks connected thereto, each of said flanks being provided with a first step spaced from said end portion, so as to form first surface portions inclined from the pointed end portion towards the first step, on the engaging teeth of the engaging sleeve and of the gear, the improvement wherein the tooth flanks of the engaging sleeve are provided with a second step spaced from said first step so that second surface portions are formed which are inclined from the first step towards the second step and which have a smaller angle of inclination relative to a plane parallel to adjacent flank surfaces inside the second step than said first surface portions.