An apparatus for assembling caps having at least a supporting body of plastic material and a filter element of ceramic material, characterized in that it comprises, in combination: - a base; - a feeding station for a succession of supporting bodies, which is connected to the base; - a feeding station for a succession of filter elements, which is connected to the base and equipped with heating means configured to raise the temperature of each filter element at least at a coupling portion of filter element, the filter element being designed to be connected to a respective supporting body by said coupling portion; - a pressing station connected to the base, set up to receive a heated filter element and at least one corresponding supporting body and configured to couple them to each other by heat sealing to form a cap; - a cooling station connected to the base and designed to receive the cap formed in the pressing station for a predetermined interval of time in order to let it cool; - a testing station connected to the base, designed to receive the at least one cap from the cooling station and configured to measure values of at least one parameter representing a correct operation of the cap; - robotized handling means connected to the base and configured to operate on the supporting bodies, the filter elements and the caps in such a way as to pick them up and transport them automatically between the stations (2, 3, 5, 6, 7); - a station for preparing the supporting bodies, comprising injector means configured to distribute a line of liquid plastic material on a bottom wall of an annular chamber formed by the supporting body and intended to receive a coupling portion of a corresponding filter element, at the intersection between said bottom wall and at least one of the lateral annular walls delimiting said annular chamber. - a base; - a feeding station for a succession of supporting bodies, which is connected to the base; - a feeding station for a succession of filter elements, which is connected to the base and equipped with heating means configured to raise the temperature of each filter element at least at a coupling portion of filter element, the filter element being designed to be connected to a respective supporting body by said coupling portion; - a pressing station connected to the base, set up to receive a heated filter element and at least one corresponding supporting body and configured to couple them to each other by heat sealing to form a cap; - a cooling station connected to the base and designed to receive the cap formed in the pressing station for a predetermined interval of time in order to let it cool; - a testing station connected to the base, designed to receive the at least one cap from the cooling station and configured to measure values of at least one parameter representing a correct operation of the cap; - robotized handling means connected to the base and configured to operate on the supporting bodies, the filter elements and the caps in such a way as to pick them up and transport them automatically between the stations (2, 3, 5, 6, 7); - a station for preparing the supporting bodies, comprising injector means configured to distribute a line of liquid plastic material on a bottom wall of an annular chamber formed by the supporting body and intended to receive a coupling portion of a corresponding filter element, at the intersection between said bottom wall and at least one of the lateral annular walls delimiting said annular chamber.