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We study a relativistic model of the nucleus consisting of nucleons coupled to mesonic degrees of freedom via an effective Lagrangian whose parameters are determined by a fit to selected nuclear ground-state data. We find that the model allows a very good description of nuclear ground-state properties. Because of the relativistic nature of the model, the spin properties are uniquely fixed. We discuss variations of the parametrization and of the data which suggest that the present fit has exhausted the limits of the mean-field approximation, and discuss extensions which go beyond the mean field.