We present a theoretical analysis and numerical simulations of lateral current density fronts in bistable resonant-tunneling diodes with Z-shaped current-voltage characteristics. The bistability is due to the charge accumulation in the quantum well of the double-barrier structure. We focus on asymmetric structures in the regime of sequential incoherent tunneling and study the dependence of the bistability range, the front velocity and the front width on the structure parameters. We propose a sectional design of a structure that is suitable for experimental observation of front propagation and discuss potential problems of such measurements in view of our theoretical findings. We point out the possibility to use sectional resonant-tunneling structures as controllable three-terminal switches.