  $D=2$ free string in linear dilaton background is considered in so called
target space/world-sheet light cone gauge $ X^{+}=0,~g_{++}=0,~g_{+-}=1$. After
gauge fixing the theory has the residual Virasoro and $U(1)$ current
symmetries. The physical spectrum related to $SL_2$ invariant vacuum is found
to be trivial. We find that the theory has a nontrivial spectrum if the states
in different non-equivalent representations ("pictures") of CFT algebra of
matter fields are considered.
