  An extended version of the Maz'ya-Shaposhnikova theorem on the limit as $s\to
0^+$ of the Gagliardo-Slobodeckij fractional seminorm is established in the
Orlicz space setting. Our result holds in fractional Orlicz-Sobolev spaces
associated with Young functions satisfying the $\Delta_2$-condition, and, as
shown by counterexamples, it may fail if this condition is dropped.
