The effect of free gas on electrical submersible pump (ESP) performance is well known. At a constant rotational speed and constant liquid flow rate, a small amount of gas causes a mild head reduction when compared to the single phase liquid head. However, at higher gas rates, a drastic reduction in the head is observed. This critical condition, known as the surging point, is a combination of liquid and gas flow rates that cause a maximum in the head performance curve. The first derivative of the head with respect to the liquid flow rate changes sign as the liquid flow rate crosses the surging point. In several works on ESP two-phase flow performance, production conditions to the left of the surging region are described or reported as unstable operational conditions. This paper reviews basic concepts on stability of dynamical systems and shows through simulation that ESP oscillatory behavior may result from two-phase flow conditions. A specific drift flux computation code was developed to simulate the dynamic behavior of ESP wells producing without packers.