Sustainability Transitions Research (STR) confronts complex societal challenges by examining societal shifts and their trajectories. An emerging perspective in STR is discursive approaches, which analyse the role of discourses and discourse coalitions in shaping sustainability transitions. However, discursive approaches face challenges regarding the analysis of sustainability transition processes as complex, temporal processes of stability and change. We discuss the nature of these challenges and explore the method of discourse network analysis (DNA) as a potential solution. We extend DNA significantly by measuring distinct temporal states (phases of stability) in discourse networks and detecting phase transitions (significant changes) between these discursive states. An empirical application of this extension to the discursive networks around the introduction of a Low Emission Zone demonstrates how and when discourses and actors display significant structural shifts. This methodological innovation addresses the need for measuring stability and change in the complex, discursive, temporal dynamics of sustainability transitions.