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Several real-world libraries (e.g., reentrant locks, GUI frameworks, serialization libraries) require their clients to use the provided API in a manner that conforms to a context-free specification. Motivated by this observation, this paper describes a new technique for verifying the correct usage of context-free API protocols. The key idea underlying our technique is to over-approximate the program's feasible API call sequences using a context-free grammar (CFG) and then check language inclusion between this grammar and the specification. However, since this inclusion check may fail due to imprecision in the program's CFG abstraction, we propose a novel refinement technique to progressively improve the CFG. In particular, our method obtains counterexamples from CFG inclusion queries and uses them to introduce new non-terminals and productions to the grammar while still over-approximating the program's relevant behavior. We have implemented the proposed algorithm in a tool called CFPChecker and evaluate it on 10 popular Java applications that use at least one API with a context-free specification. Our evaluation shows that CFPChecker is able to verify correct usage of the API in clients that use it correctly and produces counterexamples for those that do not. We also compare our method against three relevant baselines and demonstrate that CFPChecker enables verification of safety properties that are beyond the reach of existing tools.