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Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely uninvestigated. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal robot walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., the center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP model. The middle layer of the proposed approach is a walking pattern generator that translates the desired global behaviors into the robot's full-body reference trajectories for all directly actuated degrees of freedom. The lowest layer is an input-output linearizing controller that exponentially tracks those full-body reference trajectories based on the full-order, hybrid, nonlinear robot dynamics. Simulations of planar underactuated bipedal walking on a swaying DRS confirm that the proposed framework ensures the walking stability under different DRS motions and gait types.