A frequency sweep proton-proton double-resonance study of spin relaxation is made in strongly coupled two spin systems (AB) formed by the protons in 2-bromothiazole (sample I) and in 2,3,4-trichloronitrobenzene (sample II). The single-resonance transitions of both these molecules exhibit broadening due to scalar coupling with nearby14N nuclei modulated by the rapid quadrupolar relaxation of the latter. A density-matrix analysis of double-resonance spectra obtained over a wide range of irradiation strengths coupled with a determination of14N resonance linewidths and approximate measurements of proton relaxation times leads to a determination of the spin-spin coupling constants of14N with the two protons, and the parameters describing the other mechanisms of proton relaxation in these molecules. It has been shown that a study of relaxation by double resonance is, in general, capable of yielding the relative signs of the coupling constants involving the14N nucleus. The results obtained may be summarized as follows: