We study the realization of the (super) conformal topological symmetry
in two-dimensional field theories. The mirror automorphism of the top
ological algebra is represented as a reflection in the space of fields
. As a consequence, a double BRST structure for topological matter the
ories is found. It is shown that the implementation of the topological
symmetry in non-critical (super) string theories depends on the matte
r content of the two realizations connected by the mirror transformati
on.