  Let (A,p_l)_{l\in\Bbb N} be a Frechet algebra. In this paper, we introduce
the concept of Segal Frechet algebra and investigate known results about
abstract Segal algebras, for Segal Frechet algebras. Also we recall the concept
of approximate identities for topological algebras and provide some remarkable
results for Segal Frechet algebras. Moreover, we verify ideal theorem for
Frechet algebras and characterize closed ideals of Segal Frechet algebra
(B,q_m)_{m\in\Bbb N} in (A,p_l)_{l\in\Bbb N}.
