This paper examines research on the individual needs of gifted children, with a special focus on underachieving gifted students, and provides results of a study of students in a 10-week after-school enrichment program in Queensland, Australia. Over 300 gifted children (ages 5-8) attended the program, and five case studies are provided using information from parent and child interviews, tutor notes, classroom observations, and video recordings. Two of the students discussed conform to standard teacher expectations of gifted students, while the others show a variety of signs of low self-esteem, withdrawn or aggressive behavior, inability to concentrate, resistance to teacher efforts to motivate, and poor peer relationships. While such traits are often associated with low achievement, these students demonstrated performance on a level with or above that of high achievers, and demonstrated no negative behaviors. It is concluded that intervention needs to recognize the importance of identification strategies, careful nurturing, and programming which reinforces opportunities for students to become autonomous yet cooperative learners. (Contains 43 references.) (PB)