  We propose a phase diagram of quasi-low-dimensional type II superconductors
in parallel magnetic fields, when antiferromagnetic fluctuations contribute to
the pairing interactions. We point out that pairing interactions mediated by
antiferromagnetic fluctuations necessarily include both singlet channels and
triplet channels as attractive interactions. Usually, a singlet pairing is
favored at zero field, but a triplet pairing occurs at high fields where the
singlet pairing is suppressed by the Pauli paramagnetic pair-breaking effect.
As a result, the critical field increases divergently at low temperatures. A
possible relation to experimental phase diagrams of a quasi-one-dimensional
organic superconductor is briefly discussed. We also discuss a possibility that
a triplet superconductivity is observed even at zero field.
