Background We examined the component skills of reading comprehension (i.e., letter sound knowledge, syllable reading fluency, decoding fluency, text or oral reading fluency and listening comprehension) and their structural relations using data from three sub-Saharan African languages with transparent orthographies in a multilingual context. Methods Data from Kiswahili (N = 946), Kikamba (N = 444) and Lubukusu (N = 499) reading assessments at the end of Grade 2 in Kenya were analysed using path analyses. Results The magnitudes of the relations were similar across the three languages with some differences amongst the languages. Total effects (regression weights), accounting for direct and indirect effects, varied across the component skills: text reading fluency (0.73 to 0.77), decoding fluency (0.49 to 0.82), letter sound knowledge (0.44 to 0.45), syllable reading fluency (-0.12 to 0.16) and listening comprehension (0.08 to 0.23). Conclusions The results indicate similar reading mechanisms across the three sub-Saharan languages.