  We investigate a collective excitation (Leggett's mode) corresponding to
small fluctuations of the relative phase of two condensates in two-band
superconductor using the effective ``phase only'' action. We consider the
possibility of observing Leggett's mode in MgB$_2$ superconductor and conclude
that for the known at present values of the two-band model parameters for
MgB$_2$ Leggett's mode arises above the two-particle threshold.
