A novel in-situ synthesis technique has previously been proposed for the synthesis of magnesium based nanocomposites, by exploiting the thermodynamic reactions, to fabricate nanoparticles in-situ during the melt processing. Although the microstructural aspects of formation of such nanocomposites have been dealt with previously, the implications of the same on the texture and hence on mechanical properties are not certain. In the present work, the evolution of crystallographic texture and its influence on tension-compression asymmetry (Tensile yield strength ÷ Compressive yield strength) and thereby, the impact on fatigue failure mechanisms is studied by comparing the behaviour of Mg-1.8Y/1.53ZnO nanocomposite and its monolithic alloy, Mg-1.8Y. The Mg-1.8Y/1.53ZnO nanocomposite revealed a very strong two component texture, not akin to the weak texture of Mg-1.8Y alloy. The texture was attributed to the loss of Y in the matrix and consumption of Y in formation of Y2O3 nanoparticles in-situ and the formation of the β1′ (Mg-Zn′) rods during extrusion. Further, this texture exhibited by the nanocomposite favoured high twinning activity under compression, thereby causing strong asymmetry in the tensile and compressive yield strengths. The fatigue tests indicated a superior performance of the nanocomposite as compared to the alloy. The deformation and damage mechanisms, when studied in correlation with the asymmetry revealed that the asymmetric materials exhibit steeper S-N curves as compared to the symmetric materials.