Using Redfield’s theory of relaxation, it is demonstrated that interference of the dipolar and quadrupolar interactions between a spin-1/2 and a spin-1 nucleus causes a frequency shift of the spin-1/2 transition coupled to the m = 0 state of the spin-1 nucleus relative to the transitions coupled to the m=+/-1 states. This frequency shift depends on the rotational correlation time : it vanishes in the fast tumbling limit and reaches a constant in the slow motion limit which coincides with the results for static powder samples. For a C-13 nucleus which is J-coupled to a directly bonded H-2, this results in an asymmetric triplet pattern for molecular motions slower than at the T-1 minimum of the spin-1 nucleus. The center component of the triplet is shifted downfield by an amount which depends inversely on the static magnetic field strength. Although rapid longitudinal relaxation of the spin-1 nucleus collapses both the J multiplet and the interference-induced splitting, the interference contribution to the line width of the spin-1/2 nucleus can only be removed in part by high-power decoupling of the spin-1 nucleus. Experimental results are demonstrated for the C-13 spectrum of perdeuterated glycerol, where the rotational correlation time is varied with temperature. Application of the theory to other nuclei indicates that dipolar/quadrupolar interference also results in additional line broadening for proteins in solution that are enriched in H-2, and for amide protons attached to N-14.