In public discourse, meaning is constantly renegotiated. Frames and other semantic structures are co-constructed in the public debate based on the contributions of many discourse participants. Over time, they incorporate new information and interpretations. As a result, time-dependent changes occur both on the level of manifest contributions and on the level of latent structures organizing discourse into meaningful frames. This article introduces a technique capable of analyzing the changing patterns of meaning in a genuinely dynamic fashion. It applies Evolutionary Factor Analysis (EFA), a recently developed technique for treating high-dimensional data with time-changing latent structure. Using EFA, we uncover evolving patterns on different levels of abstraction within our data, which represent discourse as a detailed semantic network. We investigate specific dynamics expected within dynamic discourse (e.g., emergence, evolution, consolidation, crisis) and analyze the time-changing structure and content of meaning. The methodological innovation presented in this paper allows a detailed analysis of micro-level changes organized by latent higher-level structures: It can be transferred to a variety of social phenomena organized by structures that evolve over time (e.g., public opinion, social interaction). Rendering their dynamic behavior accessible to statistical analysis, it offers new theoretical insights into their mechanics and underlying structure.