Method for modified atmosphere, vacuum or skin packaging of food products in a thermoforming machine, the method, for generating a package, comprising: • a first forward movement step in which a cover film is arranged on a product to be packaged and on a base film which supports said product, in a superposing area of the machine, and in which both films (1, 2) are moved in a first direction to a joining station of the machine which is arranged downstream of the superposing area in the first direction; • an attachment step in which both films (1, 2) are attached to one another with the product housed between them, the cooperation between a lower tool (5.1) and an upper tool (5.2) of the joining station being caused to that end, with a cavity (5.3) around the product being demarcated between both tools (5.1, 5.2) through said cooperation and the contour of said cavity (5.3) being demarcated by two longitudinal walls and two transverse walls; • a second forward movement step in which the films (1, 2) attached in the joining station are moved in the first direction to a cutting station of the machine arranged downstream of the joining station in the first direction; and • a cutting step in which at least one transverse cut is made in the films (1, 2) in a second direction which is transverse to the first direction, obtaining an individual package with the product therein; characterized in that the cover film which is arranged on the base film in the first forward movement step comprises a width greater than the width of the base film in the second direction, said films (1, 2) being arranged with respect to one another in the superposing area such that two areas of the cover film project transversely from respective longitudinal edges of the base film in said second direction, in that in the first forward movement step and in the second forward movement step a transport device only acts on the two areas of the cover film projecting transversely from the base film to cause the forward movement of both films (1, 2) in the first direction, at least between the joining station and the cutting station, in that in the attachment step the tools (5.1, 5.2) of the joining station cooperate with one another to attach the base film and the cover film to one another such that they longitudinally grip said cover film but not said base film, and gas between said films (1, 2) is injected and/or extracted through at least one of the respective access spaces that is available between each longitudinal edge of the cover film and the longitudinal wall demarcating the cavity (5.3) closer to said longitudinal edge, in that in the cutting step a longitudinal cut is made on the areas of the cover film projecting transversely from the base film, and in that, during the second forward movement step, a supporting device (8.1) keeps the films (1, 2) gripped between the joining station and the cutting station, the supporting device (8.1) being caused to move in the first direction from a first position to a second position that are spaced apart in the first direction, together and simultaneously with the forward movement of the films (1, 2), during the forward movement thereof. • a first forward movement step in which a cover film is arranged on a product to be packaged and on a base film which supports said product, in a superposing area of the machine, and in which both films (1, 2) are moved in a first direction to a joining station of the machine which is arranged downstream of the superposing area in the first direction; • an attachment step in which both films (1, 2) are attached to one another with the product housed between them, the cooperation between a lower tool (5.1) and an upper tool (5.2) of the joining station being caused to that end, with a cavity (5.3) around the product being demarcated between both tools (5.1, 5.2) through said cooperation and the contour of said cavity (5.3) being demarcated by two longitudinal walls and two transverse walls; • a second forward movement step in which the films (1, 2) attached in the joining station are moved in the first direction to a cutting station of the machine arranged downstream of the joining station in the first direction; and • a cutting step in which at least one transverse cut is made in the films (1, 2) in a second direction which is transverse to the first direction, obtaining an individual package with the product therein;