  The combination of this paper and its companion complete the classification
of monodromy groups of indecomposable coverings of complex curves
$f:X\rightarrow \mathbb P^1$ of sufficiently large degree in comparison to the
genus of $X$. In this paper we determine all such coverings with monodromy
group $G\leq S_\ell\wr S_t$ of product type for $t\ge 2$.
