The boundedness of a chaotic system is one of the fundamental concepts of dynamical systems， which plays an important role in investigating the uniqueness of singularity， global asymptotic stability， global exponential stability， estimating the Lyapunov dimension of attractors， the Hausdorff dimension of attractors， the existence of the periodic solution， its control and synchronization and so on. However， as far as the authors know， there are only a few papers dealing with bounds of highorder chaotic systems due to their complex algebraic structure. To sort this out， in this paper， we study the bounds of a highorder chaos system and a 3D Lorenzlike system arising in mathematical physics. Based on Lyapunov stability theory， we show that the solutions of two systems are bounded when t→+∞. The innovation of the paper is that we not only prove that two systems are globally bounded for all the parameters， but also give a family of mathematical expressions of ultimate bound sets of two systems with respect to its parameters. The results of this paper provide a theoretical basis for the application and circuit design of the chaotic system in engineerings.