General formulas are derived for the spin—lattice relaxation times along the static magnetic field (T1) and the rotating field (T1r) due to magnetic dipole—dipole interactions. First‐order perturbation theory is used in the calculation, and it is assumed that the spin system can be described by a temperature. The correlation functions that appear in these formulas are evaluated for the case of a spin system in which each spin has just two possible equilibrium positions. The results are used to improve Holcomb and Pedersen's calculation of dipole—dipole spin—lattice relaxation due to the motion of spin pairs that execute 180° rotational flips about their perpendicular bisecting axes. Applying the results to gypsum (CaSO4⋅2H2O) yields T1=43.4 msec at the minimum of the T1‐vs‐temperature curve for a static‐field strength B0=2348 G. The experimental value is 47±4 msec. Similarly, the calculated minimum of the T1r‐vs‐temperature curve is T1r=1.86 msec for a rotating‐magnetic‐field strength B1=20.2 G. The experimental value isT1r=1.9±0.2 msec.