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Neuroimaging studies suggest that the increment of the cognitive load associated with a specific task may induce the recruitment of a more bilateral brain network. In most studies, however, task demand has been manipulated in a static and pre-specified way, regardless of individual cognitive resources. Here we implemented a new paradigm based on a pre-experimental assessment to set up subject-specific levels of task demand and applied tDCS (transcranial direct current stimulation) to assess each hemisphere involvement in task performance. 24 young participants performed a digit span backward (DSB, complex cognitive function) and a paced finger tapping task (pFT, basic motor function) at 3 levels of subject-specific task demand ("low" 5/5 correct answers, "medium" 3/5, "high" 1/5). Anodal tDCS (20min, 1.5mA) was delivered through a target electrode (5 × 5cm) positioned to stimulate both the inferior frontal gyrus and the primary motor area over left and right hemisphere and in sham condition in three different days. A 3 (left, right, sham) × 3 (low, medium, high) mixed-model with random intercept for subjects was run with R software. As expected, in both tasks accuracy decreased with the increment of subject-specific task demand. Moreover, a significant interaction between type of stimulation and subject-specific task demand was found for the reaction times recorded during the DSB and for the accuracy in the pFT: in the most demanding conditions, right anodal tDCS significantly interfered with behavioural performance. Our results suggest that hemispheric lateralization is modulated by the subject-specific level of task demand and this modulation is not task-specific., (Copyright © 2017 Elsevier Ltd. All rights reserved.)