The paper investigates the conditions for the existence of an equilibrium solution in the energy transfer equation for well-developed ocean waves under wind influence. The authors study the balance between wind input, wave-wave interaction, and dissipation. They use a parameterization for wind input based on measurements and an algorithm for wave-wave interaction. The dissipation is assumed to be quasi-linear in the wave spectrum. The first part of the paper examines whether the Pierson-Moskowitz spectrum, a commonly assumed equilibrium spectrum, is consistent with the assumed dissipation function. They find that it is not, due to a strong angular imbalance. In the second part, they assume a specific form of dissipation and perform numerical experiments to simulate fetch-limited wave growth. They find that for certain values of the dissipation parameters, a quasi-equilibrium solution can be reached. The energy balance proposed by Zakharov and Filonenko, and Kitaigorodskii, does not lead to an equilibrium spectrum but does not approach equilibrium. One of the equilibrium solutions has a one-dimensional spectrum close to the Pierson-Moskowitz spectrum but with different angular distribution. The detailed energy balance of this equilibrium spectrum is analyzed. The study supports the qualitative structure of the energy balance inferred from earlier wave growth experiments and computations of individual source functions.The paper investigates the conditions for the existence of an equilibrium solution in the energy transfer equation for well-developed ocean waves under wind influence. The authors study the balance between wind input, wave-wave interaction, and dissipation. They use a parameterization for wind input based on measurements and an algorithm for wave-wave interaction. The dissipation is assumed to be quasi-linear in the wave spectrum. The first part of the paper examines whether the Pierson-Moskowitz spectrum, a commonly assumed equilibrium spectrum, is consistent with the assumed dissipation function. They find that it is not, due to a strong angular imbalance. In the second part, they assume a specific form of dissipation and perform numerical experiments to simulate fetch-limited wave growth. They find that for certain values of the dissipation parameters, a quasi-equilibrium solution can be reached. The energy balance proposed by Zakharov and Filonenko, and Kitaigorodskii, does not lead to an equilibrium spectrum but does not approach equilibrium. One of the equilibrium solutions has a one-dimensional spectrum close to the Pierson-Moskowitz spectrum but with different angular distribution. The detailed energy balance of this equilibrium spectrum is analyzed. The study supports the qualitative structure of the energy balance inferred from earlier wave growth experiments and computations of individual source functions.