  We present the superfield generalization of free higher spin equations in
tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n)
holonomy as a possible framework for the construction of a non-linear higher
spin field theory. Surprisingly enough, we find that the most general solution
of the supergravity constraints is given by a class of superconformally flat
and OSp(1|n)-related geometries. Because of the conformal symmetry of the
supergravity constraints and of the higher spin field equations such geometries
turn out to be trivial in the sense that they cannot generate a `minimal'
coupling of higher spin fields to their potentials even in curved backgrounds
with a non-zero cosmological constant. This suggests that the construction of
interacting higher spin theories in this framework might require an extension
of the tensorial superspace with additional coordinates such as twistor-like
spinor variables which are used to construct the OSp(1|2n) invariant
(`preonic') superparticle action in tensorial superspace.
