This longitudinal study investigated to what extent the acquisition of cognates among bilingual children depends on the degree of cross-language similarity and intensity of exposure to the tested language, and whether children's sensitivity to cognates with different degrees of cross-language similarity changes over time. For three consecutive years, 120 Frisian-Dutch bilingual children were tested on their Frisian receptive vocabulary. The sample was split into three groups that differed with respect to intensity of exposure to Frisian at home. In the receptive vocabulary task, cross-language similarity was systematically manipulated through four cognate categories, differing in their degree of overlap between Frisian and Dutch. The results showed a gradual cognate facilitation effect for children with a low intensity of exposure to Frisian. The higher the degree of cross-language similarity, the better their performance. This implies that the co-activation of the two languages depends on the degree of cross-language similarity. Over time, their performance improved the most on non-identical cognates with a cross-linguistic phonological regularity between Frisian and Dutch. This suggests that as they grow older, children with a low intensity of exposure to Frisian become better at recognizing regularities in the overlap of the Frisian and Dutch phonological systems.