  We consider periodic matrix-valued Jacobi operators. The spectrum of this
operator is absolutely continuous and consists of intervals separated by gaps.
We define the Lyapunov function, which is analytic on an associated Riemann
surface. On each sheet the Lyapunov function has the standard properties of the
Lyapunov function for the scalar case. We show that this function has (real or
complex) branch points, which we call resonances. We prove that there exist two
types of gaps: i) stable gaps, i.e., the endpoints are periodic and
anti-periodic eigenvalues, ii) unstable (resonance) gaps, i.e., the endpoints
are resonances (real branch points). We show that some spectral data determine
the spectrum (counting multiplicity) of the Jacobi operator.
