Let $\cal A$ be a Banach algebra and $\sigma$ and $\tau$ be continuous endomorphisms on $\cal A$. In this paper, we introduce and study the concept $(\sigma, \tau)-$ideal amenability for $\cal A$. In the following, we will investigate the concepts $(\sigma, \tau)-$weak amenability and $(\sigma, \tau)-$ideal amenability for the unitization of Banach algebras.
