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We explore theoretically how nonlocal corrections in the description of a metal affect the strong coupling between excitons and plasmons in typical examples where nonlocal effects are anticipated to be strong, namely, small metallic nanoparticles, thin metallic nanoshells, or dimers with narrow separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalized nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations, the influence of nonlocality is rather limited, as in most occasions the width of the Rabi splitting remains largely unaffected and the two hybrid modes are well distinguishable. We discuss how this behavior can be understood in view of the popular coupled-harmonic-oscillator model, while we also provide analytic solutions based on Mie theory to describe the hybrid modes in the case of matryoshka-like single nanoparticles. Our analysis provides an answer to a so far open question, that of the influence of nonlocality on strong coupling, and is expected to facilitate the design and study of plexcitonic architectures with ultrafine geometrical details.