  We consider the operators $H_0=M_0^{-1}(x) P(D)$ and $H =M^{-1} (x) P(D)$
where $M_0 (x)$ and $M (x)$ are positively definite bounded matrix-valued
functions and $P(D)$ is an elliptic differential operator. Our main result is
that the wave operators for the pair $H_0$, $H$ exist and are complete if the
difference $ M(x)-M_0(x)=O(|x|^{- rho})$, $ rho>d$, as $|x| to infty$. Our
point is that no special assumptions on $M_0(x)$ are required. Similar results
are obtained in scattering theory for the wave equation.
