The measurement of transverse resistivity of Nb Ti composite wires has shown already the existence of a resistive barrier between SC filaments and the copper matrix. The electric and thermal resistances of this barrier are respectively much higher than those of copper matrix and this barrier is expected to have an influence on the cryogenic stability of composite wires. The transverse and longitudinal resistivities are measured for Nb Ti composite wires which were heat-treated at different temperatures from 300 ยฐ C to 600 ยฐ C. These measurements show that the barrier grows with the heat-treatment temperature. From the experimental results, the effect of the barrier on cryogenic stability is estimated to be negligibly small for the composite wire which is heat-treated under the normal condition. As for Nb3Sn composite wires, two different structures of composite wires, each of which has a tantalum or niobium diffusion barrier, are studied and the same :asurements as on Nb Ti composite wires are carried out. The results obtained indicate that the transverse resistivity depends appreciably on the structure of composite wires and that the larger transverse resistivity reduces not only the cryogenic stability, but also requires a larger transfer length at a current lead junction.