It is shown by electron paramagnetic resonance (EPR) and superconducting quantum interference device (SQUID) magnetometry that two spin systems coexist in conducting layers of the quasi-2D organic metal (BEDO-TTF)(2)ReO(4)·H(2)O: delocalized moments of charge carriers (holes), I(epr)(300 K) = 1.62 × 10(-4) emu mol(-1), and localized moments on BEDO-TTF(+1), χ(p)(300 K) = 4.25 × 10(-4) emu mol(-1). The phase transition Me-Me' at T(c) = 203 K is detected in paramagnetic relaxation, EPR amplitude and resistivity. Magnetic susceptibilities, I(epr) and χ(p), are not sensitive to the transition. Due to fine rearrangement of ReO(4) linked by H(2)O, the electronic spectrum becomes inhomogeneous. Below the transition exchange-coupled localized states within the metallic phase are observed. On cooling, the concentration of delocalized moments gradually decreases, contributing to a localized spin system. The phenomenon is interpreted in terms of short-range antiferromagnetic (AFM) interactions via conducting electrons. Below 14 K the AFM coupled states decay, and paramagnetism of local moments is recovered.