Grid-forming wind storage systems can actively support grid frequency. This frequency response (FR) process requires energy support. However, the FR energy is provided by either wind turbine or energy storage, easily resulting in the excessive variation of rotor speed or lifetime decline of energy storage. Therefore, the FR energy should be cooperatively provided by multiple FR resources. This paper analyzes the FR mechanism of different FR resources, such as rotor, dc-capacitor and energy storage. On this basis, the principle of cooperative control is designed. Then, based on the three-loop control structure of the machine side converter, this paper proposes a cooperative FR control strategy, which can reduce the number of responses of the energy storage, extending its lifetime. In addition, the proposed control can significantly reduce the rate of change of rotor speed. Finally, the cooperative effect of the proposed control is verified by simulations.