Let $G$ be finitely generated group (i.e $G= <S>$ $S=\{ s_1, ..., s_n\}$) and $\varphi:G\times M\longrightarrow M$ is an action then $f:G\longrightarrow M$ is called $\delta$- pseudo orbit if $d(f(sg), \varphi(s,f(g)))<\delta$ for every $s\in S$, $g\in G$. How can we define asymptotic pseudo orbit for action $\varphi:G\times M\longrightarrow M$?