We investigate the monotonic growth of longitudinal interlayer magnetoresistance <$E R Bar sub zz (B sub z )>, analytically and numerically in the self-consistent Born approximation. We show that in a weak magnetic field the monotonic part of <$E R Bar sub zz (B sub z )> is almost constant and starts to grow only above the crossover field <$E B sub c>, when the Landau levels (LL) become isolated, i.e., when the LL separation becomes greater than the LL broadening. In higher field <$E B sub z~>> >>~B sub c>, <$E R Bar sub zz (B sub z )~symbol Х~B sub z sup {1 "/" 2}> in agreement with previous works.