Strong pseudo-amenability is introduced and the properties of this generalized notion of pseudo-amenability is discussed. As an application, we investigate strong pseeudo-amenability of some semigroup algebras. For instance, we show that for a Brandt semigroup S = M0(G, I), ℓ1(S) is strong pseudo-amenable if and only if G is amenable and I is finite. Also strong pseudo-amenability of some Munn algebras is studied here.
