We consider a new realization of magnetoelastic interactions in low-dimensional magnetic systems. We show that low-dimensional spin systems are unstable with respect to the spontaneous appearance of alternating distortions of the positions of the three-dimensional nonmagnetic atoms (ligands), that surround the magnetic ions. Those distortions are supplemented by the spontaneous onset of alternating effective g factors of the magnetic ions in the phase with short-range interactions. We discuss the possibility of observing the effect in an uniform external magnetic field, which in the situation considered produces both magnetization and staggered magnetization of the magnetic subsystem. The connection of the proposed theory with recent experiments on effectively low-dimensional magnetic systems (organic spin chains, heavy-fermion compounds, rare-earth molybdates) is discussed. PACS: 75.10.Jm, 71.70.Fk, 71.70.Ej Interest in electron systems with substantial coupling between the charge, spin, and orbital degrees of freedom of the electronic and elastic subsystems of a crystal has grown considerably during the last decade. The prime examples of the manifestation of such cooperative effects are the phenomena of collosal magnetoresistance of manganites, non-Fermiliquid behavior of some heavy-fermion compounds, spin-Peierls and charge ordering behaviors in inorganic systems and unconventional superconductivity [1]. The Jahn-Teller effect [2] is probably the oldest known manifestation of such a coupling. Here the degeneracy of the orbital states of a molecule is removed by the deformation of the latter. The cooperative Jahn-Teller effect reveals itself in a structural phase transition. It has been observed in a number of compounds [3]. In the spin-Peierls transition also the degeneracy of the electronic (spin, not orbital) subsystem of a onedimensional (1D) spin chain is removed due to the coupling with a longitudinal phonon of the 3D crystal lattice. A spin gap is opened for the lowlying spin excitation. On the other hand, the corresponding phonon mode possesses softening (Kohn anomaly). Some of magnetic compounds with the essential coupling between spin, orbital, and elastic subsystems manifest paramagnetic spin behavior with two essentially inequivalent magnetic centers at low temperatures (which are higher, though, than the temperature of the phase transition to magnetically ordered 3D state). Often the latter has not been observed [4][5][6][7][8][9]. For higher temperatures the inequivalence between the two magnetic centers smears out. The presence of inequivalent magnetic centers in low-dimensional quantum spin systems is usually connected with slightly different local surrounding of two types of magnetic ions and involves either staggered g factors of the magnetic ions [4] (another case pertains to two anisotropic g tensors canted with respect to the principal axis [8] or the Dzyaloshinskii-Moriya coupling in crystals without mirror magnetic symmetry [10]. Low-lying spin excitations are gapless for these low-di...