  A microscopic theory for the spin triplet Cooper pairing in
non-centrosymmetric superconductors like CePt_3Si and CeTSi_3 (T=Rh, Ir) is
presented. The lack of inversion symmetry leads to new anomalous spin
fluctuations which stabilize the triplet part in addition to the singlet part
originating from the centrosymmetric spin fluctuations. It is shown that both
parts have similar nontrivial momentum dependence of A_1 type. Therefore the
mixed singlet-triplet gap function has accidental line nodes on both Fermi
surface sheets which are stable as function of temperature. This gap function
explains the salient features of CePt_3Si and CeTSi_3 superconductors.
