Small ingots of Nb-Si alloys were made from high-purity, solid form (not powder) Nb and Si by arc melting and suction casting into a copper mold. Samples from these ingots were tested for the presence of a superconducting transition temperature (Tc) and were found to be super-conducting (with a Tc near 7.5 Deg. K) up to 37.5 Atomic percent silicon. Metallographic and microprobe studies to determine the superconducting phase in the system led to the discovery of an unreported compound, Nb3Si, and indicated that Nb4Si does not exist. Further investigation showed that Ta3Si also exists and that Ta4Si does not, these alloys being similarly prepared from solid-form, high-purity Ta and Si. Nb3Si and Ta3Si were found to have isomorphous tetragonal structures with parameters ao=10.21+-0.01 Oa, co=5.19+-0.01 Oa, and ao=10.17+-0.01 Oa and co=5.16+0.01 Oa, respectively. The Ta3Si pattern was found to be nearly identical to one reported by brewer for TaSi0.20+-0.05. Nb3Si was determined to be essentially a line compound which melts peritectically at 1945 deg. +- 20 Deg. C. It was found to be nonsuperconducting above 4.2 Deg. K. The superconducting phase was determined to be Nb solid solution, which was present as a Nb-Nb3Si eutectic up to 37.5 Atomic percent Si.