  In an external magnetic field B, the spins of the electron and hole will
precess in effective fields b_e + B and b_h + B, where b_e and b_h are random
hyperfine fields acting on the electron and hole, respectively. For sparse
"soft" pairs the magnitudes of these effective fields coincide. The dynamics of
precession for these pairs acquires a slow component, which leads to a slowing
down of recombination. We study the effect of soft pairs on organic
magnetoresistance, where slow recombination translates into blocking of the
passage of current. It appears that when b_e and b_h have identical gaussian
distributions the contribution of soft pairs to the current does not depend on
B. Amazingly, small inequivalence in the rms values of b_e and b_h gives rise
to a magnetic field response, and it becomes progressively stronger as the
inequivalence increases. We find the expression for this response by performing
the averaging over b_e, b_h analytically. Another source of magnetic field
response in the regime when current is dominated by soft pairs is inequivalence
of the g-factors of the pair partners. Our analytical calculation indicates
that for this mechanism the response has an opposite sign.
