Reading and writing skills are intricately associated, and their mutual influence is seen as a dynamic process during literacy development for English. However, a broader understanding of the cross-domain development of literacy would be gained by examining literacy acquisition across different languages and scripts. An advantageous approach is to examine multiple language learning in a within-person design by investigating bilinguals during the earliest phases of literacy development. In this study, we contrast bilingual children who are learning English plus an Asian script (Chinese, Malay, or Tamil) to shed some light on language-general and -specific aspects of the interrelations of literacy skills. In a longitudinal design using cross-lag analysis, 620 bilingual children were administered reading and writing (spelling) tasks for English and their other script across 3 years (kindergarten into primary school entry). Models of English reading and writing were different for the three bilingual groups: Chinese and Tamil speakers showed relational patterns similar to monolingual results, but Malay speakers showed only a later reading-to-spelling influence. Models of cross-domain relations within each additional language also revealed differences across groups, suggesting language specific aspects of literacy development. Malay, a transparent orthography, supported bi-directional influence across skills consistently, while Chinese showed only an initial bidirectional influence, and Tamil supported a later spelling-to reading influence. Finally, cross-language influences differed between bilingual groups for each skill: with a consistent mutual influence for Malay-English reading, and a mutual influence for early Chinese-English spelling and later Malay-English spelling. Findings suggest that new perspectives of cross-linguistic models of literacy development are in order.