We investigated the dimensionality and relations between L1 (a speaker's first language) and L2 (a speaker's second language) writing skills in narrative and informational genres and higher order cognitive skills--inference, perspective taking, and comprehension monitoring--for Spanish-English dual language learners in primary grades. Dimensions of written composition and higher order cognitive skills were examined, comparing nine alternative models. Data from 317 dual language learners in Grades 1 and 2 were used in confirmatory factor analysis and structural equation modeling. For the dimensionality of written composition, a unidimensional model, where writing was characterized as a single underlying construct across languages (Spanish and English) and genres (narrative and opinion), fit the data best. With regard to the dimensionality of higher order cognitive skills, data supported a bifactor model with (a) a general factor that captures common variance across languages and across inference, perspective taking, and comprehension monitoring skills and (b) specific factors by language (Spanish and English). The higher order cognition general factor was fairly strongly related to writing quality (0.59), and the relation remained even after accounting for sex, poverty status, grade level, English learner status, school, and biliterate status. These relations were similar for students in an English immersion program and in Spanish-English dual immersion programs. These results indicate potential cross-language transfer of higher order cognitive skills and the roles of higher order cognitions in written composition for Spanish-English dual language learners.