The resistive state of type-II transition-element superconductors in a high magnetic field is studied using a technique due to Maki et al. The order parameters for the individual bands have similar Abrikosov-type solutions. Assuming a common upper critical field for the two bands, it is seen that the motions of the $s$- and $d$-electron pairs are controlled by different diffusion equations. The diffusion constants for the $s$- and $d$-pair motions are obtained for a typical transition-element superconductor. It is found that the $s$-band diffusion constant is not affected by the presence of the second band, but that the $d$-band diffusion constant is affected.