The stabilities of three different RNA fragments have been measured as a function of Mg2+ concentrations, and are interpreted in terms of two different models of Mg(2+)-RNA interaction. The models presume either tight binding of ions to specific site(s) in a folded RNA, or non-specific, electrostatic binding to both folded and unfolded forms; qualitatively different predictions are made for the melting temperature dependence on ion concentration. Three different modes of Mg2+ interactions with RNA structures are distinguished. Hairpins are stabilized by completely non-specific binding, with affinities the same as or weaker than those for single strand and duplex homopolymers binding Mg2+. In contrast, a ribosomal RNA tertiary structure is stabilized by specific binding of a single ion; since no other di- or trivalent ion is as effective as Mg2+, direct coordination of Mg2+ to the RNA structure is probably taking place. A third class of sites is best analyzed by the site-specific model, but any di- or trivalent ion is as effective as Mg2+; the ion(s) are probably localized in a region of unusually high charge density. The magnitude of a Mg(2+)-induced shift in RNAtm is itself not diagnostic of specific site binding or RNA tertiary structure, since large shifts can be observed for all three interaction modes.