Researchers using different methods have converged on the result that subject relative clauses are easier to process than object relative clauses. Cross-linguistic evidence for the subject processing advantage (SPA) has come mostly from accusative languages, where the covariance of grammatical function and case prevents researchers from determining which of these two factors underlies the SPA. Languages with morphological ergativity allow for the separation of case and grammatical function, since the subject position is associated with two cases: absolutive (intransitive subjects) and ergative (transitive subjects). Prior experimental results on the processing of ergative languages suggest that grammatical function and surface case may be equally important in relative clause processing. On the one hand, as a syntactic subject, the ergative DP has a processing advantage over the absolutive object. On the other hand, the appearance of an ergative serves as a cue for the projection of the absolutive object, which gives processing preference to that object. This paper further tests these findings by examining the processing of relative clauses in Ch'ol and Q'anjob'al, two languages that mark ergativity via agreement on the predicate (head-marking). We address two main questions: (a) does the SPA hold in ergative languages? and (b) are case and agreement equally able to license grammatical functions, and if so, is this reflected in processing? With regard to (a), our results support the SPA, suggesting that it is present in both ergative and accusative languages. With respect to (b), we do not find evidence for a cueing effect associated with the ergative agreement marker. We conclude that dependent-marking is superior to head-marking in tracking grammatical function; in the absence of case cues, universal structural preferences such as the SPA become more pronounced. We also consider and reject a processing explanation for syntactic ergativity, according to which some languages categorically avoid A-bar movement of the ergative with a gap because it imposes a heavy processing load. Our results show that the processing of ergative gaps is not associated with greater cost than the processing of absolutive object gaps; this suggests that an explanation for syntactic ergativity should be sought outside processing.