The nuclear magnetic resonance spin—lattice relaxation times along the static and rotating magnetic fields, and the second moment of the nuclear magnetic resonance line shape are calculated for a system of two identical spins that undergo a hindered rotation about the perpendicular bisector of the line joining the spins. The hindered rotation treated in this model is the jumping of the spins among four equally spaced equilibrium positions, two of the positions differing in energy from the other two. For finite temperatures, this difference in energy is shown to lengthen the spin—lattice relaxation times and inhibit the narrowing of the resonance line shape.