A spindle drive for a lumbar support in a backrest structure of a motor vehicle seat includes two gliders guided on a carrier of the lumbar support. Each glider is connected to a spindle nut which is engaged with an associated thread section of a spindle. The thread sections have threads of opposite thread pitch, so that the gliders are movable in opposite directions and pivot towards and away from the carrier supporting bails of a supporting device hinged to the carrier and being adjustable substantially perpendicular to the carrier. At least one of the spindle nuts partly encompasses the spindle and can be clipped onto its associated thread section of the spindle.