  We study theoretically the Josephson effect in junctions based on
unconventional superconductors with diffusive barriers, using the
quasiclassical Green's function formalism. Generalized boundary conditions at
junction interfaces applicable to unconventional superconductors are derived by
calculating a matrix current within the circuit transport theory. Applying
these boundary conditions, we have calculated the Josephson current in
structures with various pairing symmetries. A number of predictions are made:
(a) nonmonotonic temperature dependence in d-wave superconductor/diffusive
normal metal/d-wave superconductor (D/DN/D) junctions, (b) anomalous
current-phase relation in $p $-wave superconductor/diffusive normal metal/$p$%
-wave superconductor (P/DN/P) junctions, (c) second harmonics in D/DN/D and
P/DN/P junctions, (d) a double peak structure of the critical current in D/DF/D
junctions, (e) enhanced Josephson current by the exchange field in S/DF/P
junctions. We have also investigated peculiarities of the Josephson coupling in
D/DF/D, P/DF/P and S/DF/P junctions. An oscillatory behavior of the
supercurrent and the second harmonics in the current-phase relation are studied
as a function of the length of the diffusive ferromagnet.
