We have measured the effect of an applied magnetic field on the current through thin films of two different organic conjugated polymers that have previously shown to exhibit magnetoresistance, poly(9,9-dioctyl-1,4-fluorenylenevinylene) and poly(9,9-dioctyl-2,7-fluorenylenevinylene). The results show that the magnetic field releases trapped charges from inside the material and enhances the current. We have also performed optical absorption experiments on these polymer films under applied voltage and magnetic field. The results show that the magnetic field produces a change in the optical absorption in the low-energy range associated with deep traps and only under conditions when these traps are likely charged. These two results provide a str...