Conduction electron spin résonance study is presented together with static susceptibility, thermopower and IR absorption measurements for (BEDT-TTF) 4Hg3-δCl8. It is shown that the strong exchange interactions lead to a single ESR line broadened by the spin-orbit coupling ; the role of two-dimensionality of the salt is emphasized. The two-dimensionality of the spin ordering is also stated. The anomalies of the ESR parameters near 80 K may be associated with a phase transition caused probably by the deformation of the incommensurate Hg sublattice. Our study confirms that the anisotropy of the spectral (IR, ESR) properties does not necessarily agree with that of the transport properties of the organic metal.