With precise U-234, Th-230, and Pa-231 data available, Th-230 and Pa-231 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 Th-230 and Pa-231 concentrations are effectively zero. The systematics of concordia plots in relation to models of variation in delta(234)U, episodic U loss or gain, continuous U loss or gain, and continuous U-234, Th-230 and Pa-231 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. Copyright (C) 1998 Elsevier Science Ltd.