This paper demonstrates systematic cross-linguistic differences in the electrophysiological correlates of conflicts between form and meaning ("semantic reversal anomalies"). These engender P600 effects in English and Dutch (e.g. [Kolk et al., 2003] and [Kuperberg et al., 2003]), but a biphasic N400--late positivity pattern in German (Schlesewsky and Bornkessel-Schlesewsky, 2009), and monophasic N400 effects in Turkish (Experiment 1) and Mandarin Chinese (Experiment 2). Experiment 3 revealed that, in Icelandic, semantic reversal anomalies show the English pattern with verbs requiring a position-based identification of argument roles, but the German pattern with verbs requiring a case-based identification of argument roles. The overall pattern of results reveals two separate dimensions of cross-linguistic variation: (i) the presence vs. absence of an N400, which we attribute to cross-linguistic differences with regard to the sequence-dependence of the form-to-meaning mapping and (ii) the presence vs. absence of a late positivity, which we interpret as an instance of a categorisation-related late P300, and which is observable when the language under consideration allows for a binary well-formedness categorisation of reversal anomalies. We conclude that, rather than reflecting linguistic domains such as syntax and semantics, the late positivity vs. N400 distinction is better understood in terms of the strategies that serve to optimise the form-to-meaning mapping in a given language.