Evaluation of the convergence bound in the frequency domain for Volterra series expansion of nonlinear systems described by NARX models is studied. This provides new convergence criteria under which the nonlinear system of interest has a convergent Volterra series expansion, and the new criteria are expressed explicitly in terms of the input magnitude, model parameters, and frequency variable. The new convergence criteria are firstly developed for harmonic inputs and then extended to multi-tone and general input cases. Based on the theoretical analysis, a general procedure for calculating the convergence bound is provided. The results provide a fundamental basis for nonlinear signal processing using the Volterra series theory.