Magnetic dipole-dipole interactions in a nuclear-spin system can lead to ordering of the spins only at temperatures $\sim10^{-6}$ $^\circ$K. For nuclear antiferro- and ferromagnetic states to occur in this case, however, only the nuclear-spin system must be cooled to this temperature. This becomes possible in a number of cases, since the spin-lattice relaxation time becomes large enough already at a crystal-lattice temperature $\sim0.1-0.3^\circ$K, and the spin system is well insulated from the lattice. We discuss dynamic methods of obtaining near-zero positive and negative spin temperatures in a solid by adiabatic demagnetization of the nuclear-spin system. A simple theory is described, which yields the possible ordered configurations of the spins in the crystals. Methods of observing ordered states are described, together with the results of recent experiments that confirm the onset of nuclear antiferro- and ferromagnetic states.