In most languages, most of the syntactic dependency relations found in any given sentenceare PROJECTIVE: the word–word dependencies in the sentence do not cross each other. Somesyntactic dependency relations, however, are NON-PROJECTIVE: some of their word–worddependencies cross each other. Non-projective dependencies are both rarer and more computationallycomplex than projective dependencies; hence, it is of natural interest to investigatewhether there are any processing costs specific to non-projective dependencies, andwhether factors known to influence processing of projective dependencies also affect nonprojectivedependency processing. We report three self-paced reading studies, togetherwith corpus and sentence completion studies, investigating the comprehension difficultyassociated with the non-projective dependencies created by the extraposition of relativeclauses in English. We find that extraposition over either verbs or prepositional phrasescreates comprehension difficulty, and that this difficulty is consistent with probabilisticsyntactic expectations estimated from corpora. Furthermore, we find that manipulatingthe expectation that a given noun will have a postmodifying relative clause can modulateand even neutralize the difficulty associated with extraposition. Our experiments rule outaccounts based purely on derivational complexity and/or dependency locality in terms oflinear positioning. Our results demonstrate that comprehenders maintain probabilisticsyntactic expectations that persist beyond projective-dependency structures, and suggestthat it may be possible to explain observed patterns of comprehension difficulty associatedwith extraposition entirely through probabilistic expectations.