We present electron spin resonance results on three different conducting phases of the organic conductor based on the planar molecule BEDT-TTF (bis(ethylenedithio)tetrathiafulvalene) and the anion ReO4 in different stoichiometries. Both the paramagnetic susceptibility χ as well as the ESR-linewidth ΔHpp may be used to classify the magnetic behaviour in terms of known behaviour of other organic metals. They indicate that the 2:1 phase, which under pressure becomes superconducting, has an anion-ordering assisted metal-insulator transition near 80 K and that the 3:2 phase has a Peierls transition at 88 K, below which two ESR lines are resolved. A third phase, which includes solvent in the crystal lattice, shows no evidence of a transition. © 1984.