The influence of antiferromagnetic order on the superconductivity in the non-centrosymmetric heavy fermion compound CePt3Si and related materials is discussed. Based on our RPA analysis for the extended Hubbard model two phases could be stabilized by a spin fluctuation induced pairing, with either dominantly p-wave or d-wave symmetry. The antiferromagnetic order plays an essential role for the low-energy physics, in particular, for the appearance of line nodes in the gap and the enhancement of spin susceptibility below Tc. Various properties and possible phase diagrams under pressure are analyzed. The present experimental situation suggests that the p-wave phase is most likely realized in CePt3Si.