The phenomenon of limited bilingual language proficiency is reported to have negative academic and/or cognitive consequences, especially among Mexican-American minority language students. Where such students have been diagnosed, fears of concomitant congitive retardation are also expressed. Research was undertaken to understand the phenomenon better and to investigate its possible cognitive/academic consequences. The study defined the meaning of knowing a language, described bilingualism, and discussed bilingualism and cognitive development. The subjects for the investigation were Mexican-American third grade students in Santa Clara County (California) School districts. Analyses of all the test data used in the study indicated that no two language proficiency tests gave the same information about a child, and that the measure of communication skills was the best predictor of achievement. The results of the investigation do not lend support to the idea that limited bilingual language proficiency is widespread. Results also indicate that, among students who do exhibit this dual language limitation, no cognitive deficits are found. (AMH)