  We provide dual sufficient conditions for subtransversality of collections of
sets in an Asplund space setting. For the convex case, we formulate a necessary
and sufficient dual criterion of subtransversality in general Banach spaces.
Our more general results suggest an intermediate notion of subtransversality,
what we call weak intrinsic subtransversality, which lies between intrinsic
transversality and subtransversality in Asplund spaces.
