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An analysis of the behavior of concentric circular dislocation glide loops of opposite sign lying on parallel slip planes has been performed by numerical methods. At large loop radii, a critical stress exists above which the loops may pass one another. This stress decreases as the slip plane spacing between the loops increases or as the loop radii increase. Below the critical passing stress the loops become coupled. In the absence of a lattice friction stress the coupled loops continuously shrink and ultimately vanish. If, on the other hand, such a friction stress exists, there also exists a critical loop radius above which the coupled loops remain permanently stuck within the crystal.