  The phase space of an integrable, volume-preserving map with one action and
$d$ angles is foliated by a one-parameter family of $d$-dimensional invariant
tori. Perturbations of such a system may lead to chaotic dynamics and
transport. We show that near a rank-one, resonant torus these mappings can be
reduced to volume-preserving "standard maps." These have twist only when the
image of the frequency map crosses the resonance curve transversely. We show
that these maps can be approximated---using averaging theory---by the usual
area-preserving twist or nontwist standard maps. The twist condition
appropriate for the volume-preserving setting is shown to be distinct from the
nondegeneracy condition used in (volume-preserving) KAM theory.
