A method of fabricating a reinforced thermoplastic composite part comprises moving a laminate of reinforcing fibers embedded in a thermoplastic matrix for sequential operations through a heating station and then a forming station. The heating station is used to soften the thermoplastic matrix in a portion of the laminate while the forming station is used to impart a geometry to a portion of the laminate whose thermoplastic matrix had just been softened. The softening and the forming are performed simultaneously on different portions of the laminate.