A consistent phenomenological approach is used to show that a true long-range order can exist in two-sublattice two-dimensional antiferromagnets (AFM) and ferrites closed to the compensation point. The effect is due to the long-range component of dipole forces. A similar result was obtained earlier for ferromagnets by Maleev [Sov. Phys. JETP43, 1240 (1976)], who suggested that the Mermin–Wagner theorem may not be valid for interactions decreasing in proportion to1/R3or more slowly. It is found that the effect exists in the case of magnets with completely identical sublattices (AFM) only due to some types of the Dzyaloshinskii–Moriya interaction. For example, it is observed for AFM with an even (in Turov’s sense) principal axis and is absent otherwise. For a magnet with nonidentical sublattices, the effect can take place only for ferrites, i.e., for sublattices that are not compensated in the exchange approximation. The effect of stabilization of long-range order disappears at the point of compensation of magnetic moment. If this point does not coincide with the point of compensation of spin angular momentum, the intensities of fluctuations are nonmonotonic functions of temperature. The obtained estimates for the phase transition temperature are compared with experimental results. ©1998 American Institute of Physics.