This study presents new data about the cross-language application of the Late Closure principle (Frazier, 1978), whose universality was put in question by data from Spanish (Cuetos & Mitchell, 1988). Using sentences containing a restrictive relative clause unambiguously modifying the first or the second noun of a complex NP (os cúmplices do ladrão/o cúmplice dos ladrões que fugiram), this study compares the behavior of Brazilian and European Portuguese speakers participating in a self-paced reading task. The data confirm that, in early phases of processing, attachment preferences are driven by a locality principle such as Late Closure. Based on a review of studies on Portuguese, Spanish and other Romance languages, we argue that the high- versus low-attachment difference across languages emerges cleanly only in off-line tasks, such as questionnaire studies, thus limiting the types of explanations for the crosslinguistic differences. We also advance an explanation for the high attachment preferences found in unspeeded questionnaire studies based on the Implicit Prosody Hypothesis (Fodor, 1998a, 2002).