Magnetic properties of BiFe0.7Mn0.3O3 (with a Neel temperature (T-N) of 425 K) and BiFe0.6Mn0.4O3 (with T-N = 350 K) were investigated by magnetic measurements between 5 and 400 K. They crystallize in space group Pnma with the root 2a(p) x 4a(p) x 2 root 2a(p) superstructure (a(p) is the parameter of the cubic perovskite subcell) with a = 5.57800(9) angstrom, b = 15.7038(3) angstrom, and c = 11.22113(16) angstrom for BiFe0.6Mn0.4O3. Both compounds show magnetization reversal or negative magnetization phenomena. However, it was found that the magnetization reversal is dependent on magnetic prehistory of a sample and measurement protocols. No magnetization reversal was observed when virgin samples were measured below T-N. Magnetization reversal effects appeared only when the samples were cooled in small magnetic fields from temperatures above T-N or after the samples were magnetized. The exchange bias effect or a shift of isothermal magnetization curves, depending on the measurement conditions, was also observed. The exchange bias changes its sign as a function of temperature and cooling conditions. Our findings allowed us to propose the extrinsic origin (related to sample inhomogeneities) of the magnetization reversal effect in these two compounds.