Monitoring a complex process often involves keeping an eye on hundreds or thousands of sensors to determine whether or not the process is stable. We have been working with dynamic data from an oil production facility in the North sea, where unstable situations should be identified as soon as possible. Motivated by this prob- lem setting, we propose a general model for classification in dynamic domains, and exemplify its use by showing how it can be employed for activity detection. We con- struct our model by using well known statistical techniques as building-blocks, and evaluate each step in the model-building process empirically. Exact inference in the proposed model is intractable, so in this paper we experiment with an approximate inference scheme.