A fundamental consideration in the analysis and design of nonlinear systems using Volterra series theory is ensuring that both the excitation amplitude and system parameters lie within appropriate bounds to guarantee the convergence of the Volterra series expansion. This chapter presents a systematic investigation into the parametric convergence boundaries of the Volterra series for nonlinear systems modeled by the Nonlinear AutoRegressive with eXogenous inputs (NARX) framework. The system output is expressed in a definitive analytical form, influenced not only by the input amplitude but also by the input's energy content and waveform characteristics. The proposed methodology introduces refined convergence criteria that incorporate model parameters, the maximum input amplitude, and a factor representing the total input energy or waveform shape. This advancement is particularly significant for practical applications, as a nonlinear system may exhibit chaotic behavior under a simple single-tone excitation, yet remain stable under multi-tone inputs of identical amplitude. To the best of our knowledge, this work presents the first closed-form expression for the parametric convergence bounds of Volterra-type nonlinear systems, moving beyond traditional power series-based approaches.