An offshore flow system is designed to operate at steady state. However, it is possible that this condition does not exist. The stability of an offshore flow system depends on the set of parameters that defines the operational state and can be numerically determined. The stationary solution is given as initial condition for the numerical simulation; if the numerical solution does not go away from the initial condition with time, the stationary solution is stable and it is the system steady state. If the numerical solution goes away with time, the stationary state is unstable, there is no steady state and an oscillatory solution develops. As a numerically cost efficient alternative to time simulations, the linear stability theory is a powerful technique to identify the stable and unstable regions. This paper presents the main features of a stability solver developed for oil production systems. Numerical results are presented for two oil fields. Stability maps are obtained and compare to field data. The comparison showed an excellent agreement with the operational conditions presented.