  The incoherent regime of Multiple Andreev Reflections (MAR) is studied in
long diffusive SNS junctions at applied voltages larger than the Thouless
energy. Incoherent MAR is treated as a transport problem in energy space by
means of a circuit theory for an equivalent electrical network. The current
through NS interfaces is explained in terms of diffusion flows of electrons and
holes through tunnel and Andreev resistors. These resistors in diffusive
junctions play roles analogous to the normal and Andreev reflection
coefficients in OTBK theory for ballistic junctions. The theory is applied to
the subharmonic gap structure (SGS); simple analytical results are obtained for
the distribution function and current spectral density for the limiting cases
of resistive and transparent NS interfaces. In the general case, the exact
solution is found in terms of chain-fractions, and the current is calculated
numerically. SGS shows qualitatively different behavior for even and odd
subharmonic numbers, and the maximum slopes of the differential resistance
correspond to the gap subharmonics. The influence of inelastic scattering on
the subgap anomalies of the differential resistance is analyzed.
