The resistive switching effects in composite films containing polyfunctional polymers, such as derivatives of carbazole (PVK), fluorene (PFD), and polyvinyl chloride (PVC), and also graphene particles (Gr) and graphene oxide (GO), the concentration of which in the polymer matrices varied in the range from 1 to 3 wt % corresponding to the percolation threshold in such systems, have been studied. The analysis of the elemental composition of the investigated composites by means of X-ray photoelectron spectroscopy have shown that the oxidation degree of Gr in GO is about 9 to 10%. It has been established that a sharp conductivity jump characterized by S-shaped current-voltage curves and the presence of their hysteresis occurs upon applying a voltage pulse to the Au/PVK (PFD; PVC): Gr (GO)/ITO/PET structures, where ITO is indium tin oxide, and PET is poly(ethylene terephthalate), with the switching time, t, in the range from 1 to 30 μs. The observed effects are attributed to the influence of redox reactions taking place on the Gr and GO particles enclosed in the polymer matrix, and the additional influence of thermomechanical properties of the polymer constituent of the matrix.