The D = 2 free string in the linear dilaton background is considered i
n the so-called target space/worldsheet light-cone gauge X(+) = 0, g(+) = 0, g(+-) = 1. After gauge-fixing, the theory has the residual Vir
asoro and U(1) current symmetries. The physical spectrum related to th
e SL(2)-invariant vacuum is found to be trivial. We find that the theo
ry has a non-trivial spectrum if the states in different nonequivalent
representations (''pictures'') of CFT algebra of matter fields are co
nsidered.