  A theoretical model for quasiparticle and Josephson tunneling in multiband
superconductors is developed and applied to MgB2-based junctions. The gap
functions in different bands in MgB2 are obtained from an extended Eliashberg
formalism, using the results of band structure calculations. The temperature
and angle dependencies of MgB2 tunneling spectra and the Josephson critical
current are calculated. The conditions for observing one or two gaps are given.
We argue that the model may help to settle the current debate concerning
two-band superconductivity in MgB2.
