In Content and Language Integrated Learning (CLIL) programmes, students learn content knowledge and a second/foreign language (L2) simultaneously. It follows that both content and language are assessed, although research on how to do so remains scarce. This study explores the interplay between cognitive and linguistic demands of CLIL assessments. Having analysed over 4900 questions in Science/Biology textbooks, workbooks and examination papers in Hong Kong, we observed that junior secondary assessments were dominated by low-level cognitive (i.e. recall of knowledge) and linguistic (i.e. no production or word-level production) demands, whereas senior secondary assessments required higher-order thinking skills (i.e. application and analysis of knowledge) expressed in sentences or even texts. Also, based on the analysis of 70 junior secondary students' performance in school examination papers, we noticed a potential hindrance of linguistic demands to students' performance in CLIL assessments. These findings together underscore the integral role of language in CLIL assessments and raise questions about the adequacy of existing pedagogical practices in preparing students to tackle both cognitive and linguistic demands in CLIL assessments, particularly when they proceed to higher grade levels where the demands in both dimensions leap. These have significant implications for CLIL assessment design, pedagogy and teacher education.