Let $\cal A$ be a Banach algebra and $\sigma$ and $\tau$ be continuous endomorphisms on $\cal A$. In this paper, we introduce the notion of $(\sigma, \tau)-$approximate contractibility of Banach algebra as an extension of $\sigma-$contractibility. Also, we investigate the relationship between $(\sigma, \tau)-$contractibility and $(\sigma, \tau)-$approximate contractibility. Finally, we define the notions of $(\sigma, \tau)-$neo-unital and $(\sigma, \tau)-$essential for a Banach ${\cal A-}$module $\cal X$ and we find the relationship of them.
