A high-quality nonwoven product is manufactured by making use of an intermediate product in which the majority of fibers are distributed in two orientations which form an angle with each other. The intermediate product is fed to a spreading and lap-forming machine (13A, 13B) which deposits the intermediate product in alternate pleats on its delivery belt so as to form a lap of superposed layers such that the majority orientations of the fibers within each layer form an angle with the majority orientations of the fibers of the contiguous layers, and the lap is subjected to a fixing treatment, for example by means of a needle-punching machine (14A, 14B).