  We investigate the vortex state in a two-band superconductor with strong
intraband and weak interband electronic scattering rates. Coupled Usadel
equations are solved numerically and the distributions of the pair potentials
and local densities of states are calculated for two bands at different values
of magnetic fields. The existence of two distinct length scales corresponding
to different bands is demonstrated. The results provide qualitative
interpretation of recent STM experiments on vortex structure imaging in MgB_2.
