The angular distribution of yradiation fro111 an asse~nbly of nuclei oriented by the magnetic h.f.s. method can be very much modified by interactio~ls between the radioactive ions and other paramagnetic ions in the crystal. In order to calculate the effect of these interactions, an operator r is derived which represents the angular distribution of 7-rays frorn a radioactive nucleus. The angular distribution a t any temperature is given by Spur(rp), where p is the statistical rnatrix e x p ( -@ / k~) / S~u r [ e x~( -@ / k~) ] , @ being the Harniltonian for the whole crystal. For a high temperature approximation, p is expanded in powers of 1/T. I t is found that, for align~nent by the magnetic 11.f.s. method, the first term which contains interaction parameters is that in 1/T', and an expression is given for the contribution of interactio~ls to this term.At very low temperatures, perturbation theory is used to estimate the effect of interactions on the lowest nuclear energy state, and hence on the angular distribution of 7-rays. It is found that, if an external magnetic field is applied along a principal axis of the g-tensor of the radioactive ions, interactions have no influence on the angular distribution of 7-rays in the limit of large fields. I t is also shown that Bleaney's restriction, that for a successful nuclear orientation experiment the broadening of the levels should be less than the hyperfine splitting, is not necessary in this case.'Manuscript