We became interested in gifted children with difficulties based on the number of children who were addressed to our outpatient units for behavioral problems such as Attention Deficit Hyperactivity Disorder, scholastic problems or symptoms of depression, and for whom we identified a high intellectual potential. This article treats in particular Attention Deficit Hyperactivity Disorder (ADHD) which is observed for certain gifted children and can cover a depression and lead to school failure. How can ADHD in gifted children be interpreted? Based on our clinical experience and the literature, we propose that this disorder stem from need for external and internal stimulation. Several hypotheses concerning this idea will be then discussed, notably concerning their therapeutic implications.