According to von Mises criterion for compatible deformation, 5 independent slip systems are required for compatible deformation. In magnesium, the primary basal or prism slip systems are not capable of accommodating tension or compression along the c-axis. Stress applied along the c-axis is believed to be accommodated by deformation along the <c+a> -<11-2-3> directions. It is generally accepted that the activation of <c+a> slips is critical for achieving high ductility in magnesium. The excellent high temperature ductility of magnesium alloys is attributed to the activation of <c+a> slips as it is believed that the difference in the critical resolved shear stress required for the operation of basal and <c+a> slips decreases with increasing temperature. The pursuit of <c+a> slips has been one of the hottest subjects in magnesium research in the last two decades. Although <c+a> slips are considered to be fundamental modes of plastic deformation in magnesium, direct observations of their operations have unfortunately been unsuccessful. Yet their dislocation core structures have never been established. In the present investigation, high purity magnesium single crystals were deformed in compression along their c-axis at 20, 200, 300, 400 and 500C and at a strain rate of 10-3/s, to a strain beyond fracture. The results showed no activation of <c+a> slips under the tested conditions. The physical impossibility of <c+a> slips is discussed in the paper, together with criticisms of von Mises Criterion and possible mechanisms of strain accommodation in the plastic deformation of polycrystalline magnesium alloys.