The thermodynamics of systems of nuclear spins coupled by dipolar interactions is investigated under fast magic-angle spinning. It is shown experimentally and theoretically that, although the two-spin quasi-invariant-the dipolar Hamiltonian-is averaged out, a dipolar quasi-invariant exists, resulting from 'three-spin' terms in the series development of the effective Hamiltonian which rules the spin system evolution. The related nuclear spin order. here called the pseudo-dipolar order, is studied as well as its saturation by the sample rotation and its thermal mixing with the Zeeman order by weak radio-frequency irradiation. (C) 2002 Elsevier Science B.V. All rights reserved.