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