In a process and apparatus for the production of hollow bodies from thermoplastic material, the walls of the hollow bodies are of a laminate structure having at least first and second layers, by means of extrusion blow molding, the pressure within the extrusion head and more particularly at the location at which the laminate is formed by the discharge of flows of material from a storage chamber in the head is maintained within limits such as to avoid disturbing the laminate to such an extent as to have an adverse effect on its function. The pressure at the time of a transition between filling and emptying of the storage chamber and between emptying and filling of the storage chamber is maintained substantially at a pressure level which approximately corresponds to the storage chamber emptying pressure.