A natural definition of q-deformation of Virasoro and superconformal a
lgebras is proposed. New Lie algebraic symmetries are shown to describ
e the lattice version of the original theory. On the classical (Poisso
n brackets) level these two-loop algebras are shown to be isomorphic t
o the Faddeev-Takhtadjan-Volkov lattice Virasoro algebra.