  Equivalence relations or, more general, quasiorders (i.e., reflexive and
transitive binary relations) $\rho$ have the property that an $n$-ary operation
$f$ preserves $\rho$, i.e., $f$ is a polymorphism of $\rho$, if and only if
each translation (i.e., unary polynomial function obtained from $f$ by
substituting constants) preserves $\rho$, i.e., it is an endomorphism of
$\rho$. We introduce a wider class of relations -- called generalized
quasiorders -- of arbitrary arities with the same property. With these
generalized quasiorders we can characterize all algebras whose clone of term
operations is determined by its translations by the above property, what
generalizes affine complete algebras. The results are based on the
characterization of so-called u-closed monoids (i.e., the unary parts of clones
with the above property) as Galois closures of the Galois connection
End-gQuord, i.e., as endomorphism monoids of generalized quasiorders. The
minimal u-closed monoids are described explicitly.
