This work reveals a special feature of nonlinear systems arising from enzyme–catalysed reactions: system coordination restricts the formation of dynamical states. Due to the feature of enzyme saturation, each term of the governing mass–balance equations for an enzyme–catalysed reaction system has an upper limit. This can be incorporated into system coordination conditions. For an autonomous system and at a critical value of enzyme activity, the solutions of the governing equations qualitatively change: from a stable oscillatory state to a non–convergent state. Correspondingly, the average reaction rates discontinuously jump. It has been found that such dependence of oscillatory states on enzyme activities is due to the restriction of system coordination conditions to the formation of dynamical states. During some stages of an oscillatory period, two periodically varying concentrations may reach such values that the conditions of system coordination cannot be maintained. For a forced enzyme–catalysed reaction system, the effects of periodically varying input on a stable focus have been examined. Like many other forced nonlinear systems, the emergence of dynamical states depends on both forcing frequency and amplitude. However, due to the restriction of system coordination, dynamical states only emerge in a certain range of forcing amplitude and frequency, beyond which no convergent states exist. Implications of the theoretical results for understanding nonlinear systems of enzyme–catalysed reactions are discussed.