In a method of joining two workpieces (10, 16) without extraneous materials to produce a workpiece 25 which is joined over a joining area (24) which is formed by two fully adjoining surfaces (13, 13') of the two workpieces (10, 16), with the first workpiece (16) being of plastic and the second workpiece (10) being of a material different from plastic, a strong bond is achieved even when the coefficients of thermal expansion of the workpieces are different by activating at least the surface (13') of the first workpiece (16) by irradiation with high-energy radiation in a first step, bringing the surfaces (13, 13') of the workpieces (10, 16) into contact in a second step and pressing the two workpieces (10, 16) against one another at room temperature, in particular at a temperature of from 15.degree. C. to 30.degree. C., to join them at the surfaces (13, 13').