  In this paper we focus on functions of the form $A^n\rightarrow
\mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$,
and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These
mappings are called \emph{multivalued functions}, and they generalize total and
partial functions. We study Galois connections between these generalized
functions and ordered pairs $(R,S)$ of relations on $A$ and $B$, respectively,
called \emph{constraints}. We describe the Galois closed sets, and decompose
the associated Galois operators, by means of necessary and sufficient
conditions which specialize, in the total single-valued case, to those given in
the author's previous work [M. Couceiro, S. Foldes. On closed sets of
relational constraints and classes of functions closed under variable
substitutions, Algebra Universalis 54 (2005) 149-165].
