Machine for stretching films made of thermoplastic material simultaneously in the longitudinal direction and in the transverse direction, comprising: - a heating tunnel for heating the plastic material of the film to be stretched; - two endless paths for the circulation of grippers for gripping the lateral edges of the film located on either side of the course of the film; - each path has an inner longitudinal portion, extending partly inside the heating tunnel, and an outer longitudinal portion, extending outside this heating tunnel, each inner longitudinal portion being formed by a pair of guide rails (5i, 5e), one of which being referred to as "inner", in other words closer to the edge of the film, and the other being referred to as "outer", in other words further away from the edge of this film; - said grippers for gripping the lateral edges of the film, which are mounted on sliders, referred to as first sliders, running along the inner guide rail; - pairs of connecting rods connecting these first sliders to second sliders running along the outer guide rail; characterised in that the machine comprises at least one assistance sub-assembly located in said heating tunnel, including: - an endless chain or belt; - a plurality of assistance members, connected to said chain or belt in succession one after the other, and - a means for driving this chain or belt, said assistance sub-assembly being arranged so that a strand of said chain or belt is located close to said sliders, and said drive means driving said chain or belt so that this strand moves near these sliders in the same direction as the direction of travel of these sliders, said assistance members being thrust members, protruding from the chain or belt on the outside thereof, and being designed so that at least one of these thrust members is brought by said strand on the course of said second sliders; and said at least one thrust member bearing against at least one of these second sliders and exerting a thrust on this slider to assist the displacement of this slider along the rail on which this slider moves. - a heating tunnel for heating the plastic material of the film to be stretched; - two endless paths for the circulation of grippers for gripping the lateral edges of the film located on either side of the course of the film; - each path has an inner longitudinal portion, extending partly inside the heating tunnel, and an outer longitudinal portion, extending outside this heating tunnel, each inner longitudinal portion being formed by a pair of guide rails (5i, 5e), one of which being referred to as "inner", in other words closer to the edge of the film, and the other being referred to as "outer", in other words further away from the edge of this film; - said grippers for gripping the lateral edges of the film, which are mounted on sliders, referred to as first sliders, running along the inner guide rail; - pairs of connecting rods connecting these first sliders to second sliders running along the outer guide rail; - an endless chain or belt; - a plurality of assistance members, connected to said chain or belt in succession one after the other, and - a means for driving this chain or belt, said assistance sub-assembly being arranged so that a strand of said chain or belt is located close to said sliders, and said drive means driving said chain or belt so that this strand moves near these sliders in the same direction as the direction of travel of these sliders, said assistance members being thrust members, protruding from the chain or belt on the outside thereof, and being designed so that at least one of these thrust members is brought by said strand on the course of said second sliders; and said at least one thrust member bearing against at least one of these second sliders and exerting a thrust on this slider to assist the displacement of this slider along the rail on which this slider moves.