Experiments in cognitive neuroscience build a setup whose set of controlled stimuli and rules elicits a cognitive process in a participant. This setup requires researchers to decide the value of quite a few parameters along several dimensions. We call ‘’contextual factors’’ the parameters often assumed not to change the cognitive process elicited and are free to vary across the experiment’s repetitions. Against this assumption, empirical evidence shows that many of these contextual factors can significantly influence cognitive performance. Nevertheless, it is (...) not entirely clear what it means for a cognitive phenomenon to be context-sensitive and how to identify context-sensitivity experimentally. We claim that a phenomenon can be context-sensitive either because it is only triggered within a specific context or because different contexts change its manifestation conditions. Assessing which of these forms of context-sensitivity is present in a given phenomenon requires a criterion for individuating it across contextual variations. We argue that some inter-level experiments that, within the mechanistic approach to explanation, are required to identify relations of constitutive relevance between a phenomenon and a mechanism, are also necessary for individuating the phenomenon across its contextual variations. We articulate a criterion according to which behavioral variations across contexts indicate different phenomena if and only if the mechanistic activities, components and/or organizational properties recruited in each context are different. We support this approach by showing how it is applied in paradigmatic studies addressing cognitive performance differences resulting from contextual variations of task features, such as stimulus type and response modality. Finally, we address the challenge that a form of context-sensitivity possessed by the so-called ‘multifunctional mechanisms’ is incompatible with our proposal because it entails that the same mechanism can be recruited in different contexts to produce different phenomena. We examine key cases of multifunctionality and argue that they are consistent with our proposal because a single mechanism can have different components, activities and/or organizational properties in different contexts. Thus, these modifications may not affect the identity of a mechanism, and they could explain how it produced different phenomena in those contexts. (shrink)