We investigate theoretically the photonic band structure of one-dimensional superlattices (SL) composed of alternating anisotropic layers with their principal axes oriented at arbitrary directions. The dispersion relation of second order is calculated analytically by using the 4 x 4 matrix method which is based on the boundary conditions of the electric and magnetic fields at each interface. It is shown that such structures can exhibit coupled electromagnetic modes between transverse magnetic TM and transverse electric TE modes, and dispersion curves that do not exist in superlattices composed only of isotropic layers. For a given value of the wave vector k(||) (parallel to the layers), the dispersion curves (frequency omega) versus k(B) (where k(B) is the Bloch wave vector of the per-iodic system along the axis of the superlattice) are illustrated. Specific applications of these results are given for the case of the biaxial superlattice. We show that with an appropriate choice of the superlattice parameters an absolute (or omnidirectional) band gap for these coupled electromagnetic waves can be obtained. The band gap width depends on the anisotropic parameters of the media forming the SL. (c) 2005 Elsevier B.V. All rights reserved.