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While elastic metasurfaces offer a remarkable and very effective approach to the subwalength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. This work introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase gradient profiles that are function of the wavenumber of the incident wave.The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semi-analytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.