  We consider $S$-operations $f \colon A^{n} \to A$ in which each argument is
assigned a signum $s \in S$ representing a "property" such as being
order-preserving or order-reversing with respect to a fixed partial order on
$A$. The set $S$ of such properties is assumed to have a monoid structure
reflecting the behaviour of these properties under the composition of
$S$-operations (e.g., order-reversing composed with order-reversing is
order-preserving). The collection of all $S$-operations with prescribed
properties for their signed arguments is not a clone (since it is not closed
under arbitrary identification of arguments), but it is a preclone with special
properties, which leads to the notion of $S$-preclone. We introduce
$S$-relations $\varrho = (\varrho_{s})_{s \in S}$, $S$-relational clones, and a
preservation property ($f \mathrel{\stackrel{S}{\triangleright}} \varrho$), and
we consider the induced Galois connection
${}^S\mathrm{Pol}$-${}^S\mathrm{Inv}$. The $S$-preclones and $S$-relational
clones turn out to be exactly the closed sets of this Galois connection. We
also establish some basic facts about the structure of the lattice of all
$S$-preclones on $A$.
