The acquisition of Standard English by speakers of other languages and by speakers of non-standard dialects seems to differ (1) in motivation, (2) in the perception of Standard English, (3) in the social significance of Standard English, (4) in the cultural heritage and its influence on man's identity and self-respect, (5) in the source language/dialect as a system, (6) in deep structures, and (7) in matters of performance. Because they differ in more ways than they agree, their teaching methodologies should not be the same. A modified ESOL approach is suggested for teaching Standard English to speakers of Black English: this teaching should be based on a cross-disciplinary approach that helps the learner overcome the barriers resulting from sources other than linguistic ones. Major emphasis should be placed on the fact that the speaker of non-standard English is a native speaker of the language; rather than seeking competence in a language unknown to him, he wishes to acquire new ways of performing in the same language. Discussed is the State University of New York College at Cortland's graduate program in English sociolinguistics for prospective and experienced English teachers, which offers training in both English for speakers of other languages and Standard English for speakers of a non-standard dialect, with special attention on the latter. (AMM)