Let $p >0$. An operator $T\in {\Cal L}({\Cal H})$ is said to be {\it $p$-posinormal} if $(TT^*)^p \le \mu (T^*T)^p$ for some $\mu> 1$. In this paper, we prove that if $T$ is $p$-posinormal then $T^n$ is also $p$-posinormal for all positive integer $n$. Moreover, we prove that if $T=U|T|$ is $p$-posinormal for $0