This paper presents a model featuring both endogenous growth and endogenous cycles. It explains how entrepreneurial choice regarding innovation within an existing leading technology or the search for a new leading technology, contributes to the existence of long waves. A major contribution of the model is that with time, the periodicity of long waves will, on average, become shorter. The intuition behind the shortening of the long wave is simple; if an endogenous growth approach is adopted, and economic growth results in the accumulation of knowledge which increases the productivity of resources in the R&D sector, then a faster pace of innovation is an implied result of the higher growth outcome. As the pace of innovation rises, the exploitation of successive leading technologies becomes more rapid, causing a shortening of the long wave.