  The paper presents the bosonic and fermionic supersymmetric extensions of the
structural equations describing conformally parametrized surfaces immersed in a
Grasmann superspace, based on the authors' earlier results. A detailed analysis
of the symmetry properties of both the classical and supersymmetric versions of
the Gauss-Weingarten equations is performed. A supersymmetric generalization of
the conjecture establishing the necessary conditions for a system to be
integrable in the sense of soliton theory is formulated and illustrated by the
examples of supersymmetric versions of the sine-Gordon equation and the
Gauss-Codazzi equations.
