Exposure and efficiency are main determinants of immigrants' second language acquisition. In some studies also interactions between these two concepts have been reported but the empirical results are rather inconsistent and there has been no theoretical foundation of this interaction effect. But the existence and direction of this interaction may have serious consequences since it has direct implications for language learning programs. The determinants exposure and efficiency have recently been integrated in an expected utility framework by Esser (2006a, 2006b), which allows clear predictions about the impact of the concepts as well as their interdependences. The interaction between exposure and efficiency is tested empirically with German data from the project 'Preschool Education and Educational Careers among Migrant Children'. The theoretically derived hypothesis of a positive interaction between the two concepts can be verified. This indicates a Matthew effect which means that children who already have an advantage (e.g. have a higher efficiency) can benefit more from an additional positive condition (like more exposure). The multiplicative link of the two concepts also implies that a learner cannot reach a higher level in the second language, if just one of the determinants is very low.