Language development is not completed when children enter primary school. As the comprehension of connectives (such as although, despite) is important for understanding and producing academic texts and, thus, relevant for school success, we investigated its development and influential factors across primary school age on the basis of a newly developed and validated test instrument. Drawing on a German sample of N = 627 children (57.6 % language minority learners) in Grades 2 to 4, results of growth curve models showed students’ initial level of the comprehension of connectives to be negatively related to its growth rate. Additional analyses revealed this association to be due mainly to parental socioeconomic status (SES) rather than children’s language background. Particularly, parental SES and children’s receptive grammar impacted initial level as well as growth rate of connective comprehension. Our results indicate the need for early and continuous sensitization of children for the register of academic language especially in the group of children from low socioeconomic background.