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The aim of the study was to investigate the problem solving processes of gifted students as they solve different non-routine mathematical problems. Twelve Jordanian gifted students (6 males and 6 females) were tested in this study. These students who achieved 90% or more in the final school mathematics test were randomly selected from year 9 in Maan governorate. Each student was required to think about a method aloud before solving six non-routine problems, followed by individual interviews for four students (2 males and 2 females). The problems focused on arithmetic, algebra, and geometry. Then the researchers analyzed students' written solutions. The analysis is based on Polya´s four steps model (1990): understanding, selecting the planning, carrying out the plan, and verifying or checking the answer. We found that in general, the students were aware about mathematical problem solving steps and different strategies to solve the problems. [ABSTRACT FROM AUTHOR]