We synthesized a new compound of CeRhGe2 with the orthorhombic CeNiSi2-type structure. By measuring the electrical resistivity, magnetic susceptibility, magnetization, specific heat, and neutron scattering for single crystals, CeRhGe2 was found to order antiferromagnetically below T-N = 7.6 K with an ordered moment of 1.3 mu(B)/Ce oriented along the magnetic easy-axis of the c-axis. Similar measurements were also carried out for CePtSi2 single crystals. From the experimental results of anisotropic magnetic susceptibility and magnetization, the crystalline electric field (CEF) scheme was obtained for CeRhGe2 and CePtSi2, together with the similar compound CeNiGe2. Furthermore, we carried out pressure experiments by measuring the electrical resistivity of CePtSi2 and CeRhGe2. In the quantum critical region where the Neel temperature becomes zero, we observed superconductivity in CePtSi2 and most likely CeRhGe2, at 1.5 and 7.1 GPa, respectively. The upper critical field of CePtSi2 was found to be highly anisotropic with respect to the three principal field directions.