The deuteron spin-lattice relaxation times,T1Q, have been measured for benzene, water and ammonia from the melting point to the liquid-vapour critical temperature and for bromobenzene over a smaller temperature range. The results are compared with previously measured proton spin-lattice relaxation times. It is shown that the deuteronT1Qvalues agree with the proton intramolecularT1values for benzene, thus confirming the separation of the dipolar and spin-rotation contributions performed by Powles and Figgins [1]. A value of the electric quadrupole coupling constant,e2qQ/th, is deduced, which agrees with the value for the molecule in the solid. For bromobenzene a value ofe2qQ/h=175±10 khz is obtained in a similar way.