Abstract
Let D, G\subset{\Bbb C} be domains, let A\subset D, B\subset G be locally regular sets, and let X:=(D\times B)\cup(A\times G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset \hat M of the envelope of holomorphy \hat X of X such that any function separately holomorphic on X\setminus M extends to a holomorphic function on \hat X\setminus\hat M. The result generalizes special cases which were studied in \cite{\"Okt 1998}, \cite{\"Okt 1999a}, and \cite{Sic 2000}.