  The conductivity of vortex lattices in multiband superconductors with high
concentration of impurities is calculated based on microscopic kinetic theory.
Both the limits of high and low fields are considered, when the magnetic
induction is close to or much smaller than the critical field strength
$H_{c2}$, respectively. It is shown that in contrast to single-band
superconductors the resistive properties are not universal but depend on the
pairing constants and ratios of diffusivities in different bands. The low-field
magneto-resistance can strongly exceed Bardeen-Stephen estimation in a
quantitative agreement with experimental data for two-band superconductor
MgB$_2$.
