  The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has
attracted much interest because it provides a tool for solving the integrable
chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic
L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev
approach, we give the explicit derivation of the eigenvectors of the component
B_n(\lambda) of the monodromy matrix for the fully inhomogeneous chain of
finite length. For the periodic chain we obtain the Baxter T-Q-equations via
separation of variables. The functional relations for the transfer matrices of
the \tau^(2) model guarantee non-trivial solutions to the Baxter equations. For
the N=2 case, which is free fermion point of a generalized Ising model, the
Baxter equations are solved explicitly.
