Double-barrier resonant-tunneling (DBRT) devices belong to a novel class of nanometer scale electronic devices with great potential applications. In these devices, the self-consistent buildup of charge due to resonant carriers in the well may lead to intrinsic bistability and hysteresis. To analyze the dynamical stability of such devices, a simple set of equations is derived from an extension of the static theory. This extension results in a model for the dynamics which cannot be linearized around a point of operation. Numerically the stability of a DBRT-structure is investigated. This non-linearizable model is compared with an earlier, more simple, linearizable model.