The neoclassical growth model focuses on factor accumulation as an engine of growth, while the neo‐Schumpetarian growth model stresses innovation. This paper argues that these two views of growth may capture different phases of a single growth experience. In the model presented below, the balanced growth path is unstable and the economy achieves sustainable growth through cycles under an empirically plausible condition, perpetually moving back and forth between two phases. One phase is characterized by higher output growth, higher investment, no innovation, and a competitive market structure. The other phase is characterized by lower output growth, lower investment, high innovation, and a more monopolistic market structure. Both investment and innovation are essential in sustaining growth indefinitely, and yet they move in an asynchronized way; only one of them appears to play a dominant role in each phase. The economy grows faster along the cycles than along the Zunstable. balanced growth path.