Literature on the so-called bilingual advantage is directed towards the investigation of whether the mastering of two languages fosters cognitive skills in the non-verbal domain. The present study aimed to evaluate whether the bilingual advantage in non-verbal skills could be best defined as domain-general or domain-specific, and, in the latter case, at identifying the basic cognitive skills involved. Bilingual and monolingual participants were divided into two different age groups (children, youths) and were tested on a battery of elementary cognitive tasks which included a choice reaction time task, a go/no-go task, two working memory tasks (numbers and symbols) and an anticipation task. Bilingual and monolingual children did not differ from each other except for the anticipation task, where bilinguals were found to be faster and more accurate than monolinguals. These findings suggest that anticipation, which has received little attention to date, is an important cognitive domain which needs to be evaluated to a greater extent both in bilingual and monolingual participants.