  In this note we study the behaviour as $s\to 0^+$ of some semigroup based
Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with
a drift. Our results generalise a previous one of Maz'ya and Shaposhnikova for
the classical fractional Sobolev spaces $W^{s,p}$, and they also underscore a
new phenomenon caused by the presence of the drift.
