  The influence of antiferromagnetic order on the superconductivity in the
non-centrosymmetric heavy fermion compound CePt$_3$Si 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 $T_{\rm
c}$. 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 CePt$_3$Si.
