  Using the functional integral method, we construct a theory of heterotic SIS
Josephson junctions between single- and two-gap superconductors. The theory
predicts the presence of in-phase and out-of-phase collective oscillation modes
of superconducting phases. The former corresponds to the Josephson plasma mode
whose frequency is drastically reduced for $\pm$ s-wave symmetry, and the
latter is a counterpart of Leggett's mode in Josephson junctions. We also
reveal that the critical current and the Fraunhofer pattern strongly depend on
the symmetry type of the two-gap superconductor.
