Rare-earth intermetallic compounds are characterised by the presence of a long-range magnetic order due to the interaction of local magnetic moments periodically located within the crystal lattice. This paper considers the possibility of forming an ordered state in cases where there is no opportunity to observe the local moment of the f-electronic shell in a traditional sense. These are, first of all, systems with a singlet ground state, as well as systems with fast spin fluctuations caused by a homogeneous intermediate-valence state of a rare-earth ion. Extensive experimental studies of these effects using neutron diffraction, neutron spectroscopy, and high-pressure studies of the magnetic phase diagram are presented and analysed, and the corresponding microscopic model representations are discussed. In particular, the possible origin of long-range magnetic order in mixed-valence compounds is analysed.