Abstract: With the increasing popularity of computerised testing, in many applications of educational testing not only the accuracy of the response is recorded, but response time as well. This additional information provides a more complex picture of the response processes. The two most important reasons to consider response times are: 1) to increase precision of the estimation of ability by using response times as collateral information; 2) to gain further insight in the underlying response processes. The hierarchical modelling framework for response times and accuracy (van der Linden, 2007) which has become the standard approach for jointly modeling response time and accuracy in educational measurement provides a clear structure for studying both response times and accuracy, but is based on a set of assumptions which may not match the complex picture that arises when realistic response processes are considered. In this presentation, the simple structure assumption and the assumption of conditional independence between response times and accuracy will be considered critically, and statistical models that relax these assumptions will be proposed. Our first model relaxes the simple structure assumption and includes cross loadings from ability to response times and allows to use more information from response times for improving precision of measurement of ability: not only differences in how much time persons use in total but also differences in how this time is allocated to different items. Second, we present a set of models that relax the assumption of conditional independence between response time and accuracy. These models can be used to explore the presence and nature of conditional dependencies.  These conditional dependences might be relevant from a substantive point of view since they shed light on interesting phenomena in response processes and possible between- and within-person differences. In addition to presenting statistical models for conditional dependence, we also look at them from a more psychological perspective and discuss different kind of phenomena that may lead to this dependence and potential ways of distinguishing between them