In this paper the process of knowledge accumulation for a particular technology is studied. Two countries, say the technology follower and the technology frontier, are considered. The frontiers knowledge growth is determined by its R&D efforts on the technology. The level of knowledge stock for the follower countryis augmented by its R&D activities for the technology and absorbing some of the external knowledge through spillover from the frontier. The extent to which the follower is able to exploit the external knowledge depends on technological gap, absorptive capacity, absorption time and degree of spillover. New concepts such as natural and enhanced degree of spillover, background and innovative knowledge and absorption speed are introduced in the present work to deeply explore the process of knowledge spillover. The factors influencing the knowledge development in the long term are simultaneously studied in an integrated structure provided by the System Dynamics approach. This framework shows the responses to the changes and provides the basis for examining the interactions among the variables over time.