Abstract: In this paper, the partial order "≤_ω￣s" is defined on Σ￣ω, and then the concepts of Sgeneralized ω-left convex language, S generalized ω-right convex language and S generalized ω-convexlanguage are introduced. The relationships between several types of convex languages and their initiallanguages arc given. Closure properties for several kinds of boolean operations on these languages areconsidered. The necessary and sufficient conditions for S generalized ω-convex languages are given.