This paper introduces and studies a new class of inflationary models called Generalized G-inflation, which is the most general single-field inflation model that still yields second-order field equations. The authors derive the background equations and explore two inflationary mechanisms: kinetically driven inflation and potential-driven slow-roll inflation. They also compute the quadratic actions for tensor and scalar cosmological perturbations, providing stability criteria and evaluating the power spectra of primordial fluctuations. The paper concludes with a discussion on the observational implications of these models.This paper introduces and studies a new class of inflationary models called Generalized G-inflation, which is the most general single-field inflation model that still yields second-order field equations. The authors derive the background equations and explore two inflationary mechanisms: kinetically driven inflation and potential-driven slow-roll inflation. They also compute the quadratic actions for tensor and scalar cosmological perturbations, providing stability criteria and evaluating the power spectra of primordial fluctuations. The paper concludes with a discussion on the observational implications of these models.