For a constant flow rate of liquid and gas in a pipe one expects the conditions along the pipe to be of a steady state nature. However, for a pipe in a hilly terrain or in an offshore pipeline-riser system, a steady state operation is often not possible, and conditions of severe or terrain slugging develop. This causes the system to operate in an undesired cyclic fashion in which alternate long liquid slugs are followed by the production of high gas flow rate. The present work deals with the condition under which steady state operation is possible. It shows theoretically that it is possible to stablize the flow by increasing the back pressure of the separator or by employing a controlled choking at the pipe exit.