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[en] We report on our recent calculations of K− and η nuclear quasi-bound states. The underlying and ηN scattering amplitudes are constructed within coupled-channel models that capture the physics of the Λ(1405) and N∗(1535) resonances, respectively. The role played by the strong energy dependence of the scattering amplitudes near threshold and the importance of self-consistent treatment of the subthreshold energy shift are discussed.