Summary: The influence of a higher-order approximation on chaotic responses of a weakly non-linear multi-degree-of-freedom system is investigated. The specific system examined is a harmonically excited spring–pendulum system, which is known to be a good model for a variety of engineering systems, including ship motions. By the method of multiple scales the original system is reduced to a second-order approximate system. The long-term behaviors of both systems are compared by examining the largest Lyapunov exponents. It is observed that the second-order approximation gives better qualitative agreement with the original system than the first-order approximation does.