This paper deals with output regulation problem for an offshore managed pressure drilling system subject to sinusoidal disturbances. The disturbance is caused by the heave motion of the floating drilling rig during pipe connections, and the objective is to maintain a constant pressure at the bottom of the well. The controller for the heave disturbance attenuation consists of three cascaded parts. First, a nonlinear inversion element is applied to invert nonlinearity of choke. Second, an adaptive compensator is designed based on internal model, and certainty equivalence principles for asymptotic rejection of time-varying heave disturbance. Third, an output feedback controller is synthesized for providing stability and improving transient performance of closed-loop system. Robust stability of closed-loop system is analyzed using edge theorem. Simulation results of the combined adaptive output regulator are presented, which show satisfactory set-point tracking and attenuation of the heave disturbance. ‡ Annulus is the space between the drill-pipe and casings. For uncased parts of the well, annulus is the space between the drill-pipe and formation. In Figure 1, the drilling fluid after leaving the drill-bit enters and flows up the annulus. § Rotating control device is used during drilling operations for making a rotating seal around the drill pipe. It isolates the well from the surrounding environment and helps to keep the pressures inside the well confined. ¶ Wellbore is the drilled hole, including the uncased part of the well. || The MPD Heave Lab is a medium scale (900 m well) experimental facility at NTNU, tailor made for testing control strategies for the heave problem.The model described by equations (3)-(9) is in form of a nonlinear strict feedback system, with an unmatched sinusoidal disturbance. By applying the following nonlinear inversion H f D 1 0 0 :