The authors give solutions for spin-lattice relaxation in NQR due to magnetic interactions, generalized for non-axial crystal fields with eta not=0. They find analytic expressions for I=3/2 and give numerical solutions for I=5/2, 7/2 and 9/2. They find that the relaxation curves change considerably with eta . Specific results are derived for relaxation due to Fermi contact in metals and other electronic hyperfine interactions. They also describe changes induced by the addition of a magnetic field, indicating fields at which standard NMR results break down.