The polypropylene-based thermoplastic fibers are uniform in cross-section, not having any degraded surface skin, and they are heat-weldable at a pressure at a temperature which is lower than the melting temperature, by virtue of internal heating due to the effect of said pressure. They are made of a first constituent with high crystallinity and at least one second constituent, compatible with the first constituent, and of crystallinity that is lower than that of the first constituent. They have a quantity of primary oxidation inhibitor lying in the range 350 ppm to 1000 ppm. Such fibers are made by spinning under conditions that avoid molecular degradation by thermal oxidation at the periphery of the fibers, in particular with cooling that is rapid immediately on leaving the extrusion head. The non-woven fabric obtained by heat-bonding such fibers is characterized by weld points that are in the form of a polymer laminate that is uniform and transparent.