A wobble riveting machine in the housing or stand of which there is arranged a lengthwise movably mounted guide body. A driving shaft having an eccentric mechanism is mounted in such guide body. According to the invention the guide body possesses a spherically constructed cradle or rocker. A wobble body member which can be pivoted to all sides by the eccentric mechanism is mounted in the cradle. At least one rivet tool or set is guided for lengthwise movement at the wobble body member, the latter being supported at the guide body.