This dissertation mainly investigates the occurrence and characteristics of density-wave instability in gas-lift wells. The investigation is based on a simplified gas-lift system, in which water and air are used as producing fluid and lifting gas respectively, and heat transfer effect is neglected. To carry out the investigation, both linear stability analysis and numerical simulation are performed. The linear stability analysis is based on a homogenous two-phase flow model and the numerical simulation is done by using a commercial available dynamic multiphase flow simulator. In this way, a crosscheck between the two methods can be made in order to gain confidence about the results. Both two methods are validated against casing heading problem before they are applied to density-wave instability study. The results show that it is possible for density-wave instability to occur in those gas-lift wells producing from depleted reservoirs. The linear stability analysis and numerical simulation give the similar parametric trend in characterizing the instability. Within the normal gas-lift operation parameter range, increasing reservoir pressure and gas injection rate increases stability, but increasing tubing diameter, productivity index and system pressure decreases stability. The instability may occur only when the well loses its capability of natural flowing. Dynamic simulation also shows that the average production rate could be significantly reduced due to the unstable gas-lift compared with the steadystate prediction. An attempt of using feedback control to stabilize the gas-lift system is also tested by using the simulator. Promising results are obtained from the test in both stabilization and increasing production. The results of this dissertation add new knowledge to gas-lift instability fundamentals and can help in diagnosing and remedying unstable gas-lift problems.