Memory limitations and probabilistic expectations are two key factors that have been posited to play a role in the incremental processing of natural language. Relative clauses (RCs) have long served as a key proving ground for such theories of language processing. Across three self-paced reading experiments, we test the online comprehension of Hungarian subject- and object-extracted RCs (SRCs and ORCs, respectively). We capitalize on the syntactic properties of Hungarian that allow for a variety of word orders within RCs, which helps us to delineate the processing costs associated with memory demand and violated expectations. Results showed a processing cost at the RC verb for structures that have longer verb-argument distances, despite those structures being more frequent in the corpus. These findings thus support theories that attribute processing difficulty to memory limitations, rather than theories that attribute difficulty to less expected structures.