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Let 
$G$ be a finite group and 
$H$, 
$K$ two subgroups of $G$. A group $G$ is said to be a mutually 
$m$-permutable product of $H$ and $K$ if 
$G\,=\,HK$ and every maximal subgroup of $H$ permutes with $K$ and every maximal subgroup of $K$ permutes with $H$. In this paper, we investigate the structure of a finite group that is a mutually $m$-permutable product of two subgroups under the assumption that its maximal subgroups are totally smooth.
