  We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\
surfaces. Semirigid surfaces occur naturally in the description of topological
gravity as well as topological supergravity. We show that such surfaces are
obtained by an integrable reduction of the structure group of a complex
supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and
their relation to the moduli spaces of $N$-\s\ \RS s.
