The study described herein is part of a larger, inclusive research study exploring the effects of model-eliciting activities (MEAs) of "real-life" situations on the development of students' mathematical creativity. This part aim at revealing students' cognitive abilities that are involved in the creative modeling processes using a qualitative analytical method. The participants were mathematically talented students, members of the "Kidumatica" math club. The data include videotapes, classroom observation and modeling products. Three core categories--appropriateness, 'mathematical resourcefulness' and inventiveness--of students' cognitive creative abilities are identified, defined and illustrated. These findings may give a better understanding of the larger concept of mathematical creativity. [For the complete proceedings, see ED597799.]