  A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a
subgroup chain $H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G$ such
that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate
finite factorised groups with submodular primary (cyclic primary) subgroups in
factors. We indicate a general approach to the description of finite groups
factorised by supersolvable submodular subgroups.
