The growing number of children in primary schools in Germany who have German as their second language (L2) has raised questions about the fairness of performance assessment. Fair tests are a prerequisite for distinguishing between L2 learning delay and a specific learning disability. We evaluated five commonly used reading and spelling tests for measurement invariance (MI) as a function of first language (German vs. other). Multi-group confirmatory factor analyses revealed strict MI for the Weingarten Basic Vocabulary Spelling Tests (WRTs) 3+ and 4+ and the Salzburger Reading (SLT) and Spelling (SRT) Tests, suggesting these instruments are suitable for assessing reading and spelling skills regardless of first language. The MI for A Reading Comprehension Test for First to Seventh Graders -- 2nd Edition (ELFE II) was partly strict with unequal intercepts for the text subscale. We discuss the implications of this finding for assessing reading performance of children with L2.