  Given a graph $G$, the number of nowhere-zero $\ZZ_q$-flows $\phi_G(q)$ is
known to be a polynomial in $q$. We extend the definition of nowhere-zero
$\ZZ_q$-flows to simplicial complexes $\Delta$ of dimension greater than one,
and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$
for certain $q$ and certain subclasses of simplicial complexes.
