With precise 234U, 230Th, and 231Pa data available, 230Th and 231Pa ages can now be tested rigorously for concordancy. If the material is not concordant, the isotopic characteristics of this material may be examined in some detail. Here, models similar to those used to describe the U-Pb system are evaluated for use in U-Th-Pa studies, for the case in which initial 230Th and 231Pa concentrations are effectively zero. The systematics of concordia plots in relation to models of variation in δ 234U, episodic U loss or gain, continuous U loss or gain, and continuous 234U, 230Th and 231Pa gain or loss are considered for the case in which initial U concentration is significant (for example, in many carbonate deposits). We also examine linear U uptake models for the case in which initial U concentration is effectively zero (for example, in teeth and bones). Such models should prove useful in interpreting data from materials that have behaved as open-systems. In particular, these models may help constrain the nature of diagenetic processes, and in some situations it may be possible to determine or constrain true ages with materials that have behaved as open-systems.