The implications of the basic assumptions of the local pinning theories for the yield stress anomaly in Ll2 alloys are discussed. An alternative theory is presented in which the superpartials on (111) cross-slip on to (010) to form long locks lying partially on (111) and (010) or completely on (010) planes (Kear-Wilsdorf locks). The ends of the locks are joined by glissile superkinks. The yield stress is controlled by superkinks bypassing the screw dislocation locks, and the increase of the yield stress with increasing temperature is due to the decrease of the lengths of superkinks. The theory accounts satisfactorily for the mechanical properties including the small strain-rate dependence of the yield stress and is consistent with electron microscope observations.