In this paper, we introduce a novel method for classifying and computing the frequencies of movement modes of intra- and interspecific dyads, focusing in particular on distance-mediated approach, retreat, following and side by side movement modes. Besides distance, other factors such as time of day, season, sex, or age can be included in the analysis to assess if they cause frequencies of movement modes to deviate from random. By subdividing the data according to selected factors, our method allows us to identify those responsible for (or correlated with) significant differences in the behaviour of dyadic pairs. We demonstrate and validate our method using both simulated and empirical data. Our simulated data were obtained from a relative-motion, biased random-walk (RM-BRW) model with attraction and repulsion components. Our empirical data were GPS relocation data collected from African elephants in Etosha National Park, Namibia. The simulated data were primarily used to validate our method while the empirical data were used to illustrate the types of behavioural assessment that our methodology reveals. Our method facilitates automated, observer-bias-free analysis of the locomotive interactions of dyads using GPS relocation data, which are becoming increasingly ubiquitous as telemetry and related technologies improve. It should open up a whole new vista of behavioural-interaction type analyses to movement and behavioural ecologists.