The purpose of this study is to investigate characteristics of limit concepts through the simultaneous use of historical and experimental epistemologies. Based on a historical epistemology which is an investigation of historical developments in a mathematical concept raised in the history of mathematics, four different developments of limit concepts were considered. Through an experimental epistemology which is an analysis of students' different stages in the development of their understanding of the mathematical concept, diverse developmental levels were scrutinized to find out how the students performed. Nine pairs of students in total were recruited and three representatives were presented. Results indicate that both historical and experimental epistemologies are useful methods for teaching mathematics along with the unpacking process and that experimental epistemologies are effective because mathematics learning is continuous.