Let CONT ≪ be the category of continuous domains and Scott continuous mappings that preserve the way-below relation on domains. Let ω-ALG ≪ be the full subcategory of CONT ≪ consisting of all countably based algebraic domains, and F I N be the category of finite posets and monotone mappings. The main result proved in this paper is that F I N is the largest Cartesian closed full subcategory of ω-ALG ≪. On the other hand, it is shown that the algebraic L-domains form a Cartesian closed full subcategory of ALG ≪.