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The main result of the present paper is : every separately-subharmonic function $u(x,y)$, which is harmonic in $y$, can be represented locally as a sum two functions, $u=u^{*}+U$, where $U$ is subharmonic and $u^{*}$ is harmonic in $y$ , subharmonic in $x$ and harmonic in $(x,y)$ outside of some nowhere dense set $S$.