  We analyze collective modes in two-band superconductors in the dirty limit.
It is shown that these modes exist at all temperatures $T$ below $T_{c}$
provided the frequency of the modes is higher than the inelastic scattering
rate and lower than the energy gaps $\Delta_{a,b}$. At low temperatures these
modes are related to counterphase oscillations of the condensate currents in
each band. The spectrum of the collective oscillations is similar to the
spectrum of the Josephson ''plasma'' modes in a tunnel Josephson junction but
the velocity of the mode propagation in the case under consideration is much
lower. At higher temperatures ($\Delta_{b}<T<T_{c}$) the spectrum consists of
two branches. One of them is gapless (sound-like) and the second one has a
threshhold that depends on coupling between the bands. We formulate the
conditions under which both types of collective modes can exist. The spectrum
of the collective modes can be determined by measuring the I-V characteristics
of a Josephson junction in a way as it was done by Carlson and Goldman.

Superconductivity