The adiabatic rapid passage (ARP) technique was applied to the study of molecular motion in solids. Second moments and spin–lattice relaxation times for solid furan and benzene were derived using ARP methods from 77 °K to the respective melting points. Unusual variations of the ARP signal height and shape with temperature were observed for these solids. These effects were interpreted as being due to the presence of short rotating frame relaxation times. New information regarding molecular motion in solid furan, as well as acetic acid-d1, was obtained. Also some quantitative statements have been made regarding the conditions required to observe an ARP signal in the solid state.