Method and apparatus for mitigating slug formation in a multiphase fluid stream flowing through a conduit. The method includes (a) determining the pressure in the conduit upstream of a slugging zone, (b) determining the pressure in the conduit downstream of the slugging zone, (c) determining the actual pressure difference across the slugging zone by subtracting the downstream pressure from step (b) from the upstream pressure from step (a), (d) determining the error between a target pressure difference and the actual pressure difference, (e) producing a signal having a first component which is proportional to the error and a second component which is proportional to the rate of change of the error over time, and (f) using the signal produced in step (e) to control the position of an adjustable choke valve located downstream of the slugging zone so as to stabilize variations arising in the actual pressure difference over time.