  We introduce a natural framework for dealing with Mourre theory in an
abstract two-Hilbert spaces setting. In particular a Mourre estimate for a pair
of self-adjoint operators (H,A) is deduced from a similar estimate for a pair
of self-adjoint operators (H_0,A_0) acting in an auxiliary Hilbert space. A new
criterion for the completeness of the wave operators in a two-Hilbert spaces
setting is also presented.
