Abstract: An asphalt laying machine having a vibrating smoothing and compacting unit, called screed assembly, and being of the type, which has a main screed with a plurality of laterally slidable extensions. In known machines said units are rigidly interconnected and their dimensions are so large that stationary vibrations may be produced in the smoothing and compacting unit, resulting in a non-homogenous asphalt course. According to the invention the smoothing and compacting unit (5) is divided into a plurality of units (12,13) having respective vibration generating means (24) and being mutually vibration isolated by means of vibration dampers (17A, 17B) ensuring a controlled, vibratory movement. The swing of each unit at the front edge preferably differs from the swing at the rear edge.