In a framing system for framing motor-vehicle bodies or sub-assemblies thereof, the body to be framed is located and clamped in position during the assembling operations by side locating and clamping structures (8). Each of these structures comprises a rigid supporting structure (82) including a base platform (82a) and a frame (81) which carries locating and clamping devices (D). The base platform (82a) is dimensioned in the direction parallel to a body conveyor line with a standard length proportionated to the length of the longest body type on which the system is to operate. Pillars (82b) for supporting the frame (81) are mounted on the platform (82a) at positions which are selected between different possible positions, displaced relative to each other longitudinally and/or transversely. Thus, the side locating and clamping structures (8) can be configured easily for different types of body and the system is able to operate on body types having also very relevant differences in length and/or width.