We present first-time measurements of the Fermi surface and low-energy electronic structure of intermetallic compounds Gd 2 PdSi 3 and Tb 2 PdSi 3 by means of angle-resolved photoelectron spectroscopy (ARPES). Both materials possess a flower-like Fermi surface consisting of an electron barrel at the Γ point surrounded by spindle-shaped electron pockets originating from the same band. The band bottom of both features lies at 0.5 eV below the Fermi level. From the experimentally measured band structure, we estimate the momentum-dependent RKKY coupling strength and demonstrate that it is peaked at the 1 2 ΓK wave vector. Comparison with neutron diffraction data from the same crystals shows perfect agreement of this vector with the propagation vector of the low-temperature in-plane magnetic order, thereby demonstrating the decisive role of the Fermi surface geometry in explaining the complex magnetically ordered ground state of ternary rare earth silicides. Ternary rare earth silicides with hexagonal crystal structure of the form R 2 PdSi 3 , where R is a rare earth atom, are known to exhibit complex magnetic behavior [1,2,3,4,5,6,7,8,9,10,11,12,13,14] Most of the R 2 PdSi 3 compounds order magnetically at low temperatures, somewhat below the Kondo minimum in the resistivity [2,3,4,5,6]. The exact type of such ordering strongly depends on the material and can be rather complicated [6,10]. The corresponding Neel temperature T N reaches maximum for the Gd (T N =21.0 K [11]) and Tb (T N =23.6 K [12]) compounds, which we have chosen as the subject of the present study. The RKKY exchange interaction that essentially determines their magnetic properties is mediated by the conductance electrons, and therefore any reasonable description of the corresponding physics is impossible without the knowledge of the Fermi surface and the low-energy electronic structure. According to our recent study [16], the sign reversal of the Hall effect observed at low temperatures in R 2 PdSi 3 [13] might be an indication of the opening of the pseudogap at some portions of the Fermi surface, as was also suggested earlier by resistivity measurements [2], again emphasizing the importance of studying the electronic structure of these materials.Nevertheless, though the single crystals of Gd 2 PdSi 3 are available since nearly a decade [3], the fermiology and the underlying band structure are still not known for any of the R 2 PdSi 3 compounds neither from momentum-resolved measurements nor from band structure calculations. Earlier photoemission experiments [17,18] were performed only on polycrystalline samples and could not therefore shed light on the dispersion of conductance electrons and the Fermi surface geometry, but have revealed that the density of states at the Fermi level is likely to be dominated by the 5d states of the rare earth atoms.Here we report an angle-resolved photoelectron spectroscopy (ARPES) investigation of the low-energy electronic structure performed on the single crystals of Gd 2 PdSi 3 and Tb 2 PdSi 3 , whose crystal st...