In this thesis classical selection principles in ditopological texture spaces have been discussed and investigated. Using open sets and their generalized forms in ditopological texture spaces, some new Menger type covering properties have been defined, and their behaviour under several types of difunctions have been investigated. The notions of almost-Menger, almost-s-Menger, almost-Rothberger, almost-Hurewicz and almost-s-Hurewicz spaces are introduced in ditopological texture spaces. Weakly Menger property along with relation to Menger and almostMenger property is studied and discussed. Semi-Hurewicz and co-semi-Hurewicz spaces are defined, their relations with and similarities from Hurewicz and coHurewicz properties are studied. Examples and counter have been provided where deem necessary.