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In this work, we propose the use of power-flow-conformal metasurfaces for the creation of dual-physics devices that can simultaneously control waves of different natures. In particular, we introduce metasurface devices that perform specified operations on both electromagnetic and acoustic waves at the same time. Using a purely analytical model based on surface impedances, we introduce metasurfaces that perform the same functionality for electromagnetic and acoustic waves and, even more challenging, different functionalities for electromagnetics and acoustics. We provide realistic topologies for practical implementations of the proposed metasurfaces and confirm the results with numerical simulations.