We have constructed a consistent system of equations for the Yang-Mills quantum-wave fluctuations in the classical Yang-Mills condensate based on canonical quantization in the Heisenberg representation. Such a quasi-classical system has been thoroughly analyzed in the conformal limit in the linear and quasi-linear approximations, both analytically and numerically. We have found that interaction between waves and condensate triggers a significant transfer or swap of energy from the condensate to the wave modes in the SU(2) gauge theory. Remarkably, a similar energy swap effect has been found in the maximally-supersymmetric N=4 Yang-Mills theory, as well as in the two-condensate SU(4) gauge theory. Such a generic feature of Yang-Mills dynamics opens up vast phenomenological implications in ultra-relativistic Yang-Mills plasma physics.