We have experimentally observed a new kind of current bistability in the time-averaged current-voltage (I-V) characteristic of doped, weakly coupled GaAs/AlAs superlattices, in which the transport is dominated by sequential resonant tunneling between adjacent quantum wells. Time-resolved current measurements show that in some cases the bistability is correlated with a subcritical Hopf bifurcation, while in other cases a discontinuous change of the current oscillation frequency is observed in the bistable region. The origin of this new bistability is attributed to a change of the space charge layer in the superlattice involving charging and discharging effects, which creates a feedback to the external bias. ©1997 American Institute of Physics.