Oxide-based resistive switching devices are a leading contender for the next generation memories. Before use, each device has to go through a conditioning process called electroformation which has been suggested to be initiated by the accumulation of oxygen vacancies. Here, experimental evidence is presented which shows that both Ta2O5-x-and TiO2-x-based crossbar devices, exhibit characteristic electronic instability leading to a reversible constriction of the current flow to a narrow filament prior to permanent change. Thus, it is asserted, electroformation is initiated through purely electronic and reversible events, to be followed later by structural changes in the material, like oxygen vacancy redistribution. Furthermore, the electronic instability responsible for electroformation also gives rise to negative differential resistance (NDR) and that this characteristics appears to involve two distinct mechanisms: a thermal one in which Joule heating causes resistance to decrease as current increases and a second electronic mechanism that appears not to require Joule heating for NDR. Using a combination of thermometry and thermal modeling, a self-consistent temperature and filament radius as a function of power are found for the 5 mu m cross-bar devices. In the thermal NDR regime, the filament appears to be similar to 500 nm in diameter and has a peak temperature of similar to 300 degrees C, while in the adiabatic regime, the estimated filament diameter is much smaller (< 50 nm) and the maximum temperature inside it exceeds 800 degrees C.