As a step towards understanding the developmental relationship between handedness and language lateralization, this longitudinal study investigated how infants (N = 21) move their hands in non-communicative and communicative situations at two weeks and at three months of age. We looked at whether left-right asymmetry in hand movements and in duration of self-touch appeared across conditions and whether the direction of asymmetry depended on the communicative nature of the situation. We found that asymmetries appeared less consistently than suggested in literature and did not only depend on the communicative nature of the situation. Instead, hand activity and self-touch patterns depended on age, the presence of the mother, the degree of novelty of the situation and the presence of an object. Our results partly support previous studies that pointed out an early differentiation of communicative hand movements versus non-communicative ones in infants. It is in terms of the amount of global hand activity, rather than in those of the laterality of hand movements that this differentiation emerged in our study. At three months, infants moved their hands more in the communicative conditions than in the non-communicative conditions and this difference appeared as a tendency already at two weeks of age.