In this paper, we study conditional preferences in abstract argumentation by introducing a new generalization of Dung-style argumentation frameworks (AFs) called Conditional Preference-based AFs (CPAFs). Each subset of arguments in a CPAF can be associated with its own preference relation. This generalizes existing approaches for preference-handling in abstract argumentation, and allows us to reason about conditional preferences in a general way. We conduct a principle-based analysis of CPAFs and compare them to related generalizations of AFs. Specifically, we highlight similarities and (...) differences to Modgil’s Extended AFs and show that our formalism can capture Value-based AFs. Moreover, we show that in some cases the introduction of conditional preferences leads to an increase in computational complexity. (shrink)