The paper addresses problems in identifying giftedness in culturally diverse populations. Among topics considered are (1) the relationship of certain performance criteria to established educational models, (2) the effect of selection processes using performance criteria on identifying children from disadvantaged backgrounds, (3) the effect of multi-behavioral criteria on selection of gifted students from minority backgrounds, and (4) effects on the process-oriented curriculum/instructional strategies on children with high potential. An expanded definition of giftedness is offered, and the literature is cited for specific performance criteria and evaluation models. The role of process-oriented curriculum is considered, and advantages of using areas of strengths or interest to develop knowledge or higher level thinking skills in another area are noted. (CL)