The basic motivation of the theory of textures is to find a convenient point-set based setting for fuzzy sets. In some recent works on textures show that they also provide a fruitful model for soft fuzzy sets. Further the category of soft fuzzy topological texture spaces is isomorphic to the category of ditopological texture spaces. The first aim of this paper is to introduce and study the notions of semi-compactness and semi-stability in ditopological texture spaces. Secondly, it is given a natural link for these concepts in soft fuzzy topological spaces by using the mentioned isomorphism.