Causal graphical models (CGMs) have become popular in nu-merous domains of psychological research for representing peoples causal knowledge. Unfortunately, however, the CGMs typically used in cognitive models prohibit representations of causal cycles. Building on work in machine learning, we pro-pose an extension of CGMs that allows cycles and apply that representation to one real-world reasoning task, namely, classi-fication. Our models predictions were assessed in experiments that tested both probabilistic and deterministic causal relations. The results were qualitatively consistent with the predictions of our model and inconsistent with those of an alternative model.