The purpose of this study was to analyze the abduction in mathematical problem-posing and problem- solving activities. Abduction is more concerned with creating new things than deduction and inductive reasoning. According to the student's rules, abduction are classified as selective and creative. Selective abduction is again classified into ‘manipulative selective abduction’ and ‘theoretical selective abduction’. Creative abduction is again classified into ‘little creative abduction’ at the level of mathematics in school and ‘big creative abduction’ at the level of academic mathematics. Four middle school sophomore students performed problem-posing activities on four tasks. As for the results of analysis on abduction types by problem-posing stages, all four abduction types were observed. But at the problem-solving stages, manipulative selective abduction and theoretical selective abduction were frequently used, while creative abduction was never used. Thus, for the education of mathematical creativity, deepening and expanding problem-posing is necessary that all the type of abduction has been expressed in the problem-posing activity.