A ring $R$ is called weakly semicommutative ring if for any $a, bin R^*=Rsetminus { 0}$ with $ab=0$, there exists $ngeq 1$ such that either $a^n
eq 0$ and $a^nRb=0$ or $b^n
eq 0$ and $aRb^n=0$. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring $R$ is a strongly regular ring if and only if $R$ is a left $SF-$ring and weakly semicommutative ring.

Keywords: weakly semicommutative rings, SF&minus,rings, strongly regular rings, semicommutative rings, Abelian rings.