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We study the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of spinfluctuation mediated pairing, and focus on the effect of coexisting chargefluctuations. We find that (i) consecutive transitions from singlet pairing toFFLO and further to $S_z=1$ triplet pairing can generally take place uponincreasing the magnetic field when strong charge fluctuations coexist with spinfluctuations, and (ii) the enhancement of the charge fluctuations lead to asignificant increase of the parity mixing in the FFLO state, where thetriplet/singlet component ratio in the gap function can be close to unity.  We propose that such consecutive pairing state transition and strong paritymixing in the FFLO state may take place in a quasi-one-dimensional organicsuperconductor (TMTSF)$_2X$.

Strong parity mixing in the FFLO superconductivity in systems with coexisting spin and charge fluctuations