A stabilization system (10) for a section of submarine pipeline (11) comprising an end restraint (15) at each end of the section of pipeline and intermediate restraints (20) between the two end restraints (15) for limiting lateral movement of the pipeline (11) at the location of the restraints (15, 20). Each end restraint (15) is adapted to be secured to the pipeline (11) to transfer axial tension generated by lateral movement of the pipeline (11) to the seabed or ground on which the end restraint is installed. Each restraint (15, 20) comprises a pair of restraint faces (21) spaced apart to define a gap (23) through which the pipeline (11) can extend. Each restraint face (21) is configured to control curvature of the pipeline (11) during lateral movement thereof. A restraint device and a method of stabilizing a submarine pipeline is also disclosed and claimed.