Model reduction by time-domain moment matching naturally extends to nonlinear models, where the notion of moments has a local nature stemming from the center manifold theorem. In this paper, the notion of moments of nonlinear models is extended to the global case and is, subsequently, utilized for model order reduction of convergent Lur’e-type nonlinear models. This model order reduction approach preserves the Lur’e-type model structure, inherits the frequency-response function interpretation of moment matching, preserves the convergence property, and allows formulating a posteriori error bound. By the grace of the
preservation of the convergence property, the reduced-order Lur’e-type model can be reliably used for generalized excitation signals without exhibiting instability issues. In a case study, the reduced-order model accurately matches the moment of the full-order Lur’e-type model and accurately describes the steady-state model response under input variations.