  We generalize the symmetry superalgebras of isometries and geometric Killing
spinors on a manifold to include all the hidden symmetries of the manifold
generated by Killing spinors in all dimensions. We show that bilinears of
geometric Killing spinors produce special Killing-Yano and special conformal
Killing-Yano forms. After defining the Lie algebra structure of hidden
symmetries generated by Killing spinors, we construct the symmetry operators as
the generalizations of the Lie derivative on spinor fields. All these
constructions together constitute the structure of generalized symmetry
superalgebras. We exemplify the construction on weak $G_2$ and nearly
K\"{a}hler manifolds.
