This article investigates English-Japanese children's code-switching (CS) from the structural point of view. Muysken categorises it into three types, that is, insertion, alternation and congruent lexicalisation. Regarding insertion, using Myers-Scotton's matrix language frame (MLF) model, for example, the matrix language (ML) of a bilingual clause can be identified and items from the other language are considered embedded. In contrast, alternation does not distinguish between the matrix and embedded languages: the speaker makes a full change from using language A to using language B. In congruent lexicalisation, on the other hand, the ML consists of two or more languages. In this article, natural data from two English-Japanese bilingual children (5;9-9;3, 3;3-6;9) are analysed primarily using the MLF model, the insertion framework, but the ML cannot be identified in 41.8% of the data. These are examined with the alternation and congruent lexicalisation frameworks. Qualitative analyses show that psycholinguistic processes and pragmatic forces underlie those non-insertional types of CS. Psycholinguistic processes of triggering and formulaic language play important roles in alternation, whereas convergence, another psycholinguistic process, leads to congruent lexicalisation. From the pragmatic point of view, English makes a pragmatic/discourse frame and Japanese expresses propositional meanings. This finding suggests that bilingual children can attribute different functions to different languages. (Contains 5 tables.)