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A detailed analysis of single dislocation loops as well as of noncoaxial passing dislocation loops in ordered and disordered alloys has been made using the piecewise approximation. The analysis shows that the passing behavior of the loops depends on y, z, and γ, where y is related to the radius of the passing loops, z is the interplanar separation, while γ is the antiphase boundary energy. When y is less than some critical value, the results show that the superlattice dislocations in ordered alloys become unstable and disassociate into partial dislocations, the motion of which generates disorder in the crystal. With a decrease of γ, superlattice dislocation instability occurs at larger y. The significance of the above results in relation to the work hardening of ordered and disordered alloys is discussed in detail.