The study was conducted to determine (1) if Anglo and Mexican American 6th-grade students differed significantly on measures of global and academic self-concepts and (2) the relationship of academic achievement to these self-concepts. A sample of 172 Anglo and 160 Mexican American students from 16 elementary schools in a southern New Mexico city was stratified by 3 socioeconomic levels. The Piers-Harris Children's Self Concept Scale and a 5-item factor-analyzed scale developed from existing research were used to measure self-concept. Student achievement was measured by teacher-assigned grades in reading, arithmetic, and social studies and by the Iowa Test of Basic Skills. A 3-way analysis of variance model (with students classified according to ethnicity, sex, and socioeconomic level) was used to test differences between students. Results indicated no significant differences between ethnic groups in terms of academic and global self-concepts, and no sex differences were found. Significant differences were found in both self-concept measures between socioeconomic levels. High socioeconomic level was associated with high self-concept and low socioeconomic level was associated with low self-concept. However, middle-socioeconomic-level Mexican American students' academic self-concept scores were almost the same as those of low-socioeconomic-level Anglo and Mexican American students. Results of actual achievement were consistent with findings of previous studies, and correlation analysis of the relationships between self-concept and achievement did not yield a consistent pattern across socioeconomic levels. (NQ)