We calculate the semiclassical magnetoresistivity rho(xx)(B) of noninteract
ing fermions in two dimensions moving in a weak and smoothly varying random
potential or random magnetic field. We demonstrate that in a broad range o
f magnetic fields the non-Markovian character of the transport leads to a s
trong positive magnetoresistance. The effect is especially pronounced in th
e case of a random magnetic field where rho(xx)(B) becomes parametrically m
uch larger than its B = 0 value.