The purpose of this study is to identify groups of gifted university students that differ in their self-concept and achievement motivation. For this, 80 students who achieved scores of the 95th percentile or higher in the Raven's Progressive Matrices test were selected. Two groups were identified in terms of their social self-concept and the competitiveness-oriented achievement motivation variables. The first group ("Protected") gathered 51 (63.7%) gifted students who exhibited high levels of social self-concept and a low level of competitiveness-oriented achievement motivation with respect to the second group ("At-risk"), which gathered 29 (36.3%) gifted students. It was concluded that "Protected" students possess affective resources that strengthen their social and academic development, whereas "At-risk" students' variables represent vulnerability factors.