This article provides an empirical analysis of a single classroom episode in which students reveal difficulties with the concept of proper time in special relativity but slowly make progress in improving their understanding. The theoretical framework used is "coordination class theory," which is an evolving model of concepts and conceptual change. The paper will focus on showing to what extent and in what sense most of the conditions and events in the data corpus seem understandable from the point of view of coordination class theory. In addition, however, some extensions of the theory are implicated, although we argue that they are "natural" extensions, improvements that extend, but do not threaten, the core theory. In particular, we observe students articulately aligning different ways of determining proper time, and we conjecture, more generally, that such a process is strongly consistent with coordination class theory and likely to be productive in other cases of conceptual change. The empirical analysis is explicitly connected to the general issue of theories and theory development in studies of conceptual change. (Contains 3 figures and 46 notes.)