In this paper we study relations between nowhere-zero $\Bbb Z_k$-
and integer-valued flows in graphs and the functions \pol{G}k and
\spol{G}k evaluating the numbers of nowhere-zero $\Bbb Z_k$- and
$k$-flows in a graph $G$, respectively. It is known that \pol{G}k is
a polynomial for $k>0$. We show that \spol{G}k is also a polynomial
and that $2^{m(G)}\pol{G}k\geq\spol{G}k\geq(m(G)+1)\pol{G}k$, where
$m(G)$ denotes the rank of the cocycle matroid of $G$.  Finally we
prove that $\pol{G}{k+1}\geq\pol{G}k\cdot k/(k-1)$ and
$\spol{G}{k+1}\geq\spol{G}k\cdot k/(k-1)$ for every $k>1$.
