  Random hyperfine fields are essential to mechanisms of low-field
magnetoresistance in organic semiconductors. Recent experiments have shown that
another type of random field --- fringe fields due to a nearby ferromagnet ---
can also dramatically affect the magnetoresistance. A theoretical analysis of
the effect of these fringe fields is challenging, as the fringe field
magnitudes and their correlation lengths are orders of magnitude larger than
that of the hyperfine couplings. We extend a recent theory of organic
magnetoresistance to calculate the magnetoresistance with both hyperfine and
fringe fields present. This theory describes several key features of the
experimental fringe-field magnetoresistance, including the applied fields where
the magnetoresistance reaches extrema, the applied field range of large
magnetoresistance effects from the fringe fields, and the sign of the effect.
