Polycrystalline samples of the intermetallic compounds R2PdGe6 (R = Pr, Nd, Gd-Er) and R2PtGe6 (R = Tb, Ho, Er) have been studied using X-ray diffraction as well as magnetometric and neutron diffraction measurements. All compounds have an orthorhombic crystal structure of the Yb2PdGe6-type (space group Cmca) and are antiferromagnetic with the Néel temperatures ranging from 4.9 K for Er2PtGe6 up to 48 K for Tb2PdGe6. The magnetic properties and specific heat data collected for Nd2PdGe6 show the presence of an additional phase transition below TN at T = 4 K. Based on the neutron diffraction data, the magnetic structures have been determined for R2PdGe6 (R = Pr, Nd, Tb, Dy, Ho) and R2PtGe6 (R = Tb and Er). Both the magnetic properties and neutron diffraction data indicate that the magnetic moment is localized on rare earth atoms. The magnetic unit cell is equal to the crystal one, however, individual compounds show different types of magnetic orderings. Magnetic moments in Pr2PdGe6 form a non-collinear antiferromagnetic structure at low temperatures with magnetic moments confined to the (001) plane. The low temperature magnetic structure in Nd2PdGe6 is a collinear antiferromagnetic one with moments parallel to the b-axis and coupled ferromagnetically within the (001) plane, while along the c-axis the moments follow the +−−+ sequence. With increasing temperature, atransition to a modulated magnetic structure is observed in Nd2PdGe6 at T = 4 K. The magnetic moments in R2PdGe6 (R = Tb, Dy, Ho) and Tb2PtGe6 assume a non-collinear antiferromagnetic order within the (001) plane with the +−+− sequence of signs of the moments in the neighboring planes along the c-axis. The Er moments in Er2PtGe6 form a collinear magnetic structure with magnetic moments oriented along the a-axis and coupled ferromagnetically within the (001) plane. Along the c-axis the moments follow the +−+− sequence. The magnetic structures determined here are discussed on the basis of the competition between the RKKY-type interactions and influence of Crystalline Electric Field.