The invention relates to an electromechanical wheel brake device with a brake caliper that is embodied of one piece with a gear housing in which a planetary roller screw drive for pressing frictional brake linings against a brake disk and a bevel gear pair for driving the planetary roller screw drive to rotate are accommodated. In order to keep a ring gear free of a force that acts axially on a nut of the planetary roller screw drive when the frictional brake linings are pressed against the brake disk, the device affixes a ring gear of the bevel gear pair in a rotationally fixed and axially mobile manner to the nut, for example by means of a multi-groove profile, and supporting the bevel gear with a separate axial bearing in the rigidly embodied gear housing.