The assembly system is for erecting internal or external walls made up from two spaced shells, with hollow service-duct-accommodating spaces between them fillable with heat and/or sound insulating materials; connectors serve for spaced fixing of the shells, engaging grooves in them or clamping them in the peripheral area. The connecting pieces incorporate battens (9-12) or small plates, parallel to each other and of a thickness corresponding to the width of the grooves (4). These combine with cross arm stems (8), sited at right angles to them, to form a monolithic component. The broad sides of the stem run in a plane passing through the joint gaps vertically to the plane of the shells.