A step-wise feeding device of containers equipped with a mouth, a plane of symmetry passing through the mouth, includes support bases and transportation means of the support bases in a feeding direction. Each support base can be associated with and dissociated from the transportation means, and each support base includes a clamping group of a container, the clamping group having a closed clamping position and an open loading and unloading position. The clamping group is a gripper-type including two side boards, sustained by supports on opposite sides of the support base, which move in a self-centering manner with respect to an axis. Each support base has a bearing plane for the bottom of the container, on which a virtual point is defined, arranged on a longitudinal axis at a fixed distance from a front end of the support base, for centering the mouth of any container arranged on the plane.