A machine for the automatic packaging of loose products or products placed in trays, with a usually heat-weldable stretch film, comprises means for unrolling sections of stretch film from a supply reel, separating said sections of film (F) into lengths appropriate for the dimensions of the product to be packaged, by transverse cutting, and positioning the sheet of film thus obtained, horizontally, in a packaging station (C), holding said sheet by the opposite longitudinal sides by means of parallel pairs (G1, G2) of superposed, synchronized belts (1, 3). One, for example the upper, of the parallel sections of the film-positioning and -conveyor belts runs on a fixed support surface (12, 13) while the other, lower one, runs on the jaws (112, 14) of clamps (P1-P5) connected to lifting or lowering means, for pushing the lower belt (1) against the upper belt (3) when required, so as to grasp the film and hold it as necessary both while it is carried along and while the film is being folded under the tray containing the product The invention provides that said clamps (P1-P5) comprise elastic means (16) and are actuated by means of cams (21) fitted on a shaft moved by rotation means (23, 24), said cams being shaped and mutually offset as appropriate, so that said clamps (P1-P5) are actuated differentially and progressively to best meet the requirements of the product packaging cycle.