Knowledge of how behaviour changes, i.e. the mechanisms underlying the effects of behaviour change interventions, is vital for accumulating valid scientific evidence and informing practice and policy-making across multiple domains. Traditional approaches to such evaluations have applied study designs and statistical models, which implicitly assume that change is linear, constant and caused by independent influences on behaviour (such as behaviour change techniques). This article illustrates limitations of these standard tools, and considers the benefits of adopting a complex adaptive systems approach to behaviour change research. It 1) outlines the complexity of behaviours and behaviour change interventions, 2) introduces readers to some key features of complex systems and how these relate to human behaviour change, and 3) provides suggestions for how researchers can better account for implications of complexity in analysing change mechanisms. We focus on three common features of complex systems (i.e. interconnectedness, non-ergodicity and non-linearity), and introduce Recurrence Analysis, a method for nonlinear time series analysis which is able to quantify complex dynamics. The supplemental website (https://git.io/Jffrm) provides exemplifying code and data for practical analysis applications. The complex adaptive systems approach opens up novel avenues for understanding and theorising about the dynamics of behaviour change.