Measurements of the current-voltage characteristics of a tunnel junction as a function of quasiparticle injection from a second tunnel junction are presented. Aluminum films (300,~ thick)are studied from the transition temperature down to about 0.35K. For a certain range of injection currents, there exists an inhomogeneous energy gap and tunnel current; the large gap approximates the undisturbed film, while the value of the small gap depends on the specific resistance of the injector junction in a regular and calculable way. There is an instability which leads to this inhomogeneous state; although these experiments cannot unambiguously determine the mechanism of the instability, we show that severe problems are found in trying to explain it in terms of existing models. On the basis of our results and analysis, the instability apparently occurs because of small spatial inhomogeneities in the films and the extremely nonlinear current-voltage characteristics of tunnel junctions, rather than intrinsic properties of the superconductor. This result does not disprove the other models of instability, but shows the limitations of tunneling for investigating the models.