Single-airfoil vanes each having an inner platform, an outer platform, and an airfoil are obtained by three-dimensionally weaving a fiber blank in a single piece, by shaping the fiber blank to obtain a single-piece fiber preform, and by densifying the preform with a matrix to obtain a vane of composite material forming a single piece with inner and outer platforms incorporated therein. A plurality of vanes is assembled together at an intermediate stage of densification to form a multi-airfoil composite material guide vane sector for a turbine nozzle or a compressor diffuser and the assembled-together vanes are bonded together.