Social interactions are a defining behavioural trait of social animals. Discovering characteristic patterns in the display of such behaviour is one of the fundamental endeavours in behavioural biology and psychology, as this promises to facilitate the general understanding, classification, prediction and even automation of social interactions. We present a novel approach to study characteristic patterns, including both sequential and synchronous actions in social interactions. The key concept in our analysis is to represent social interactions as sequences of behavioural states and to focus on changes in behavioural states shown by individuals rather than on the duration for which they are displayed. We extend techniques from data mining and bioinformatics to detect frequent patterns in these sequences and to assess how these patterns vary across individuals or changes in interaction tasks. To illustrate our approach and to demonstrate its potential, we apply it to novel data on a simple physical interaction, where one person hands a cup to another person. Our findings advance the understanding of handover interactions, a benchmark scenario for social interactions. More generally, we suggest that our approach permits a general perspective for studying social interactions.