Method for manufacturing a superconducting fiber bundle formed of a multiplicity of carrier fibers coated with a superconducting layer of a niobium compound of niobium carbonitride of the general formula NbC.sub.x N.sub.y wherein x+y is equal to or less than 1, said superconductive layer of niobium compound having a fine grained B1-structure and a mean grain size between 3 and 50 nm, which comprises reacting niobium chloride, carbon and nitrogen compounds in a CVD (chemical vapor deposition) reactor to produce the niobium compound, depositing the niobium compound from the gaseous phase on the carrier fiber in the reactor to form a superconducting layer thereon, maintaining a low total gas pressure of between 0.1 and 5 m bar, and during the deposition using plasma activation to effect grain size reduction to said grain size of between 3 and 50 nm, wherein precipitations of insulating material are deposited from the gaseous phase in the CVD reactor in the superconducting layer on all grain boundaries of the B1-structure niobium compound grains, independently of their spatial orientation, simultaneously with the niobium compound deposition.