Disclosed is a bearing system for a worm engaging with a worm wheel as part of a steering gear, wherein the bearing system comprises at least one bearing with an outer ring, an inner ring, and rolling bodies that are movably accommodated between the outer an inner rings, the bearing being pivotally arranged in a bearing seat for accommodating the outer ring of the bearing, and wherein the inner ring accommodates one of the two shaft ends of the worm in order to seat said shaft end of the worm radially in the housing of the steering gear. For an improved dampening of the worm at least one spring element, which exerts a spring force on a region of the outer ring of the bearing, is provided at the bearing, said spring force supporting a pivotal motion of the worm toward the worm wheel.