A debate exists in literature between the Goldstein's theory that Kondratieff-waves (K-waves) or Long Waves (LWs) are linked to hegemonic wars occurring in the final phase of ascending long cycles and studies that do not support this pattern. However, current theoretical frameworks have trouble explaining the sources of LWs with comprehensive and consistent arguments. This study proposes a theory that LWs are due to structural change of warfare that generates huge demand-side effects and powerful supply-side effects to support the evolution of General Purpose Technologies (GPTs) and clusters of innovation. In particular, the analysis here seems to reveal a sequential historical process that runs from wars performed by great powers, occurring in phases of instability of LWs (peak and/or trough), to GPTs and clusters of innovation in the trough of K-waves, which trigger the upward phase of new K-waves. Overall, then, the theory here can be useful for bringing a new perspective to explain, whenever possible one of the general sources of the evolution of LWs, rooted-in-war, that generates technological and economic change in society.