  In this paper, we introduce and study some notations of amenability such as
$n$-ideal amenability and $n$-weak amenability for Frechet algebra and we
examine how these concepts in Banach algebra can be generalized and defined for
Frechet algebra. We will also examine some inherited properties of $n$-ideal
and $n$-weak amenable Frechet algebra and determine the relations between $m$
and $n$-weak amenability and $m$ and $n$-ideal amenability for Frechet algebra.
Also, the relation of these new concepts of amenability of a Frechet algebra
and its unitization is investigated.
