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Magnetic ordering and indirect exchange interactions were studied in the series of hexagonal rare-earth intermetallic compounds R Ga2, where R denotes Ce, Pr, Nd, Gd, Tb, Dy, Ho, and Er. The magnetic susceptibility (χ) of polycrystalline samples was measured at low fields, from 1.5 K to about 300 K; the magnetization (M) versus applied magnetic field (H) of these polycrystalline samples and a HoGa2 single crystal was measured up to 80 kOe at low temperatures; the resistivities (ρ) of CeGa2, GdGa2, DyGa2, and HoGa2 were measured from about 1.5 K to about 300 K, at zero field. The χ(T) and M (H) results indicated that the samples order antiferromagnetically, with ordering temperatures TN ranging from 6.4 K for DyGa2 to 14.8 K for TbGa2. M (H) results for single-crystal HoGa2 show that the  direction is the easy direction and the  direction is the hard direction. High-temperature χ(T) results were fitted to the Curie-Weiss formula and the resulting effective moments are in good agreement with those expected for trivalent rare-earth ions. The paramagnetic Weiss temperatures (Θ) are positive for all the samples measured except GdGa2. The effects of magnetic ordering were observed below TN in the resistivity results. Letting the spin-disorder part of the resistivity ρs be proportional to Tn, n was determined to be about 2.0, 4.3, and 3.3 for HoGa2, GdGa2, and DyGa2, respectively. In view of the theory of Mannari for ρs, these differences may be connected with differences in the spin structures of these compounds. Ruderman-Kittel-Kasuya-Yosida (RKKY) sums have been calculated for these compounds. The negative sign of the sum is in agreement with the anitiferromagnetic properties observed in various measurements. For HoGa2, the dressed moment, due to polarization of conduction electrons, has been estimated. The theory of Nagamiya was applied to three of the compounds which can be considered as a layer compound with long-range ferromagnetic intralayer coupling and antiferromagnetic coupling between a layer and its nearest-neighbor layers. With one possible exception, the data are consistent with the theory which contains three exchange coefficients. Crystal-field-induced anisotropy appears to be important in determining the spin structures of these compounds.