  Let $D\subset \C^n,$ $G\subset \C^m$ be open sets, let
  $A$ (resp. $B$) be a subset of the boundary $\partial D$ (resp.
  $\partial G$) and let $W$ be the 2-fold boundary cross $((D\cup A)\times
B)\cup (A\times(B\cup G)).$
  An open subset $X\subset\C^{n+m} $ is said to be the ``envelope of
holomorphy" of $W$ if it is, in some sense, the maximal open set with the
following property: Any function locally bounded on $W$ and separately
holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a holomorphic
function defined on $X$ which admits the boundary values $f$ a.e. on $W.$ In
this work we will determine the envelope of holomorphy of some boundary
crosses.
