The Bloch waves, the energy bands, and the local and global densities
of states are computed for superconducting multilayers in which the Fe
rmi energy in the superconducting (S) layers, epsilon(FS), may exceed
the one in the normal (N) layers, epsilon(FN). Self-consistent pair po
tentials and their equivalent square-well representations are consider
ed. If the S-layer thickness exceeds several coherence lengths the den
sities of states exhibit the subgap peak (besides the BCS peak) and th
e Tomasch-McMillan-Anderson oscillations known from SNS junctions. The
se features, due to off-diagonal (Andreev) scattering, decrease with i
ncreasing ratio epsilon(FS)/epsilon(FN) because of the competition fro
m diagonal scattering. The temperature dependence of the energetic pos
ition of the subgap peak is weaker than that of the BCS peak. In multi
layers with S-layer thickness of the order of magnitude of one coheren
ce length and epsilon(FS)/epsilon(FN) much greater than 1, the local d
ensity of states is BCS-like in the S layers and normal-metal-like in
the N layers. This is due to electron localization in the S layers and
consistent with recent scanning tunneling microscope conductance meas
urements in YBa2Cu3O7.