  We study the formation of large-scale coherent structures (a condensate) for
a system of two weakly interacting classical waves. Using the coupled
defocusing nonlinear Schr\"odinger (NLS) equations as a representative model,
we focus on condensation in the phase mixing regime. We employ weak turbulence
theory to provide a complete thermodynamic description of the classical
condensation process. We show that the temperature and the condensate mass
fractions are fully determined by the total number of particles in each
component and the initial total energy. Moreover, we find that, at higher
energies, condensation can occur in only one component. The theory presented
provides excellent agreement with results of numerical simulations obtained by
directly integrating the dynamical model.
