A new theory for the yield stress anomaly in L12 alloys for slip on (111) is developed and applied to Ni3Al. Following Paidar, Pope and Vitek (PPV theory), it is assumed that the superpartial screws cross-slip from (111) to (010) in steps of b/2 (where b is the magnitude of the Burgers vector), but that the jogs created are highly mobile. Contrary to PPV, this leads to the formation of long cross-slipped screw segments. A second cross-slip step by the leading superpartial leads to the formation of strong edge dipole barriers at the ends of the cross-slipped superdislocations. These barriers can be unlocked by the movement of edge character superkinks joining adjacent cross-slipped screw segments, by a thermally activated mechanism which has a large athermal component. Before unlocking occurs the screws continue to cross-slip forming Kear-Wilsdorf (KW) type locks. These latter can also be unlocked by a similar mechanism, controlled by a similar athermal stress, but with a larger activation energy. The yield stress-temperature-strain-rate relation is formulated, and as in the PPV model the yield stress is controlled by the probability of cross-slip. The orientation dependence of the yield stress and the tension and compression asymmetry are therefore explained as in the PPV theory. However the new theory predicts the strain-rate dependence to be very small in agreement with experiment. The theory explains the observed variation of activation volumes with temperature in terms of two mechanisms—the unlocking of dipole barriers at low stresses/temperatures, and of KW type locks at high stresses/temperatures. The model also explains how the KW locks and other structural features observed by electron microscopy are a consequence of the deformation process.