A pneumatic multi-valve device comprising a housing, which has a housing main body with a plurality of electromagnetic valve actuators, each having coil elements arranged in the housing in a stationary manner, a core arranged in the housing, and armature elements, which can be displaced along a displacement axis in the housing in relation to the core and in relation to a pneumatic connection of the housing in response to energizing of the coil elements, wherein the displacement axes of the armature elements of the valve actuators are oriented parallel and the pneumatic connections associated with the armature elements are arranged adjacent to each other on a connection housing side, which is spaced apart from a housing back side facing away therefrom along the displacement axes, wherein the cores each have a venting bore, which is connected, for air conduction, to a venting collection channel on the side of the cores facing away from the connection housing side, which venting collection channel is bounded on the housing back side by a housing cover fastened to the housing main body, which venting collection channel is connected, for air conduction, to a venting opening of the housing, which venting opening is arranged on a housing side different from the housing back side, in particular on the connection housing side having the pneumatic connections, characterized in that the housing cover is fixed to the housing base body via an air-tight welded connection, in particular an ultrasonic or laser welded connection, wherein the venting collection channel has a trough, which is formed in the housing base body, the trough opening of which, which faces in the direction of the housing back side, is closed by the housing cover and that connection channels, which are formed by the housing base body and which are connected to the venting bores for air conduction, each lead into the trough, in particular on a trough base, in each case offset at a distance from the trough edge in the direction of the connection housing side, and a venting channel, which is embodied in the housing body and connects the venting collection opening to the venting opening and preferably extends parallel to the displacement axes, opens out offset from the trough edge at a distance in the direction of connection housing side. that the housing cover is fixed to the housing base body via an air-tight welded connection, in particular an ultrasonic or laser welded connection, wherein the venting collection channel has a trough, which is formed in the housing base body, the trough opening of which, which faces in the direction of the housing back side, is closed by the housing cover and that connection channels, which are formed by the housing base body and which are connected to the venting bores for air conduction, each lead into the trough, in particular on a trough base, in each case offset at a distance from the trough edge in the direction of the connection housing side, and a venting channel, which is embodied in the housing body and connects the venting collection opening to the venting opening and preferably extends parallel to the displacement axes, opens out offset from the trough edge at a distance in the direction of connection housing side.