  In this paper we first show that for a locally compact amenable group $G$,
every proper abstract Segal algebra of the Fourier algebra on $G$ is not
approximately amenable; consequently, every proper Segal algebra on a locally
compact abelian group is not approximately amenable. Then using the hypergroup
generated by the dual of a compact group, it is shown that all proper Segal
algebras of a class of compact groups including the $2\times 2$ special unitary
group, SU(2), are not approximately amenable.
