  Upper critical field, H_c2, in quasi-1D superconductors is investigated by
the weak coupling renormalization group technique. It is shown that H_c2
greatly exceeds not only the Pauli limit, but also the conventional
paramagnetic limit of the Flude-Ferrell-Larkin-Ovchinnikov (FFLO) state. This
increase is mainly due to quasi-1D fluctuations effect as triggered by
interference between unconventional superconductivity and density-wave
instabilities. Our results give a novel viewpoint on the large H_c2 observed in
TMTSF-salts in terms of a d-wave FFLO state that is predicted to be verified by
the H_c2 measurements under pressure.
