  Similarly to the ordinary bosonic Liouville field theory, in its N=1
supersymmetric version an infinite set of operator valued relations, the
``higher equations of motions'', holds. Equations are in one to one
correspondence with the singular representations of the super Virasoro algebra
and enumerated by a couple of natural numbers $(m,n)$. We demonstrate
explicitly these equations in the classical case, where the equations of type
$(1,n)$ survive and can be interpreted directly as relations for classical
fields. General form of the higher equations of motion is established in the
quantum case, both for the Neveu-Schwarz and Ramond series.

High Energy Physics - Theory