We continue our study of selection principles in texture and ditopological texture spaces began in . Our focus here is on the Hurewicz covering properties in texture structures and direlational uniform texture spaces. The behavior of these properties under standard operations with ditopological spaces are considered. We give game-theoretic and Ramsey-theoretic characterizations of the Hurewicz property in texture spaces, and establish relationships between selection properties of di-uniform spaces and (quasi-) uniform spaces. (C) 2017 Elsevier B.V. All rights reserved.