  We consider the inverse problem for the second order self-adjoint hyperbolic
equation in a bounded domain in $\R^n$ with lower order terms depending
analytically on the time variable. We prove that, assuming the BLR condition,
the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the
boundary uniquely determines the coefficients of the hyperbolic equation up to
a diffeomorphism and a gauge transformation. As a by-product we prove a similar
result for the nonself-adjoint hyperbolic operator with time-independent
coefficients.
