The mechanical properties and deformation behaviour of magnesium alloys are significantly influenced by the testing temperature, texture and grain size. The paper gives an overview on the influence of the grain size on the mechanical properties of Mg and Mg-2Al alloys at various temperatures. The yield stress and the fracture stress increase with decreasing grain size. It was shown that the elongation to fracture increases with inverse square root of grain size. The effect of grain size on the tensile strength and the elongation to fracture is influenced by the testing temperature. The observed grain size dependence of the elongation to fracture is explained by the activity of non-basal slip systems.