  The following result is proved: Let $D$ and $D'$ be bounded domains in
$\mathbb C^n$, $\partial D$ is smooth, real-analytic, simply connected, and
$\partial D'$ is connected, smooth, real-algebraic. Then there exists a proper
holomorphic correspondence $f:D\to D'$ if and only if $\partial D$ and
$\partial D'$ a locally CR-equivalent. This leads to a characterization of the
equivalence relationship between bounded domains in $\mathbb C^n$ modulo proper
holomorphic correspondences in terms of CR-equivalence of their boundaries.
