This study determined the degree to which the phonological and executive components of memory reflect language-specific capacities in Spanish and English vocabulary. We tested whether the memory processes in a sample of English language learners found in Grade 1 also emerged in Grade 2. For the total sample (N=90), Grade 1 English STM measures shared a common construct with Spanish STM, whereas Grade 2 STM measures were language dependent. In contrast, WM measures were language independent across grades 1 and 2. When vocabulary subgroups were analyzed, a subgroup x type of memory task emerged. The results showed that performance on Spanish and English STM tasks were a function of high and low Spanish and English vocabulary knowledge, whereas WM was not. The relationship between language-specific processes in memory was discussed.