In this talk, the existence of a continuous and bounded solution of a nonlinear Volterra integrodifferential equation is studied. In the analysis, Schaefer's fixed point theorem and Liapunov's direct method are employed. The existence of a continuous and bounded solution is shown using Schaefer's fixed point theorem, which requires an a priori bound on all such solutions of an auxiliary equation. Liapunov's direct method is then applied to obtain such an a priori bound.