A method for continuously applying on a deposition surface of an intermediate material composed of a unidirectional layer of reinforcing fibers associated on at least one of its faces to a layer of thermoplastic and/or thermosetting material, the layer(s) of thermoplastic and/or thermosetting material forming the intermediate material not representing more than 10% of the total weight of the intermediate material , and preferably representing 0.5 to 10%, and more preferably 2 to 6%, of the total weight of the intermediate material , wherein: - prior to its application, the intermediate material has undergone an operation applying spot traversing forces, performed in such a way as to traverse the total thickness of the intermediate material and accompanied by heating, leading to the at least partial melting of the thermoplastic material or the partial or complete polymerization of the thermosetting material, at the application points of traversing forces, and leading to the penetration of the thermoplastic and/or thermosetting material and creating bonding bridges in the thickness of the unidirectional layer of reinforcing fibers, preferably extending from one main face to the other of the unidirectional layer of reinforcing fibers, - the intermediate material is continuously applied, along a given movement trajectory, with simultaneous application on the intermediate material of a tension and a pressure, in such a way as to apply it on the deposition surface , the deposition being performed by applying one face (1 1 , 1 2 ) of the intermediate material in the process of being laid up to a layer of thermoplastic and/or thermosetting material on the deposition surface and/or by applying the intermediate material in the process of being laid up on the deposition surface carrying a thermoplastic and/or thermosetting material, and by activating the thermoplastic and/or thermosetting material that will exist at the interface between the intermediate material and the deposition surface , in such a way as to ensure the bond between the laid-up intermediate material and the deposition surface . - prior to its application, the intermediate material has undergone an operation applying spot traversing forces, performed in such a way as to traverse the total thickness of the intermediate material and accompanied by heating, leading to the at least partial melting of the thermoplastic material or the partial or complete polymerization of the thermosetting material, at the application points of traversing forces, and leading to the penetration of the thermoplastic and/or thermosetting material and creating bonding bridges in the thickness of the unidirectional layer of reinforcing fibers, preferably extending from one main face to the other of the unidirectional layer of reinforcing fibers, - the intermediate material is continuously applied, along a given movement trajectory, with simultaneous application on the intermediate material of a tension and a pressure, in such a way as to apply it on the deposition surface , the deposition being performed by applying one face (1 1 , 1 2 ) of the intermediate material in the process of being laid up to a layer of thermoplastic and/or thermosetting material on the deposition surface and/or by applying the intermediate material in the process of being laid up on the deposition surface carrying a thermoplastic and/or thermosetting material, and by activating the thermoplastic and/or thermosetting material that will exist at the interface between the intermediate material and the deposition surface , in such a way as to ensure the bond between the laid-up intermediate material and the deposition surface . <EOS>