The Mg-Y-Zn alloys with different contents of alloying elements are extruded at an extrusion ratio of 4:1 at 350 C. The microstructure of the alloys is of an inhomogeneous character showing fine grains produced due to dynamic recrystallization and coarse original grains elongated along the extrusion direction (ED). Moreover, Y and Zn form a long-period stacking-ordered (LPSO) phase whose volume fraction increases with their increasing content in the alloy. All investigated alloys exhibit distinct fiber textures with basal planes oriented parallel to ED. It is seen that increasing content of alloying elements leads to a weaker texture. Compression tests with concurrent acoustic emission (AE) measurements are performed along ED at room temperature and a constant strain rate in order to reveal active deformation mechanisms in the alloys and to relate them to their mechanical properties. The AE response is also discussed with respect to the volume fraction of the LPSO phase.