Vibration absorption efficiency of a variable?stiffness nonlinear energy sink ( NES ) wasinvestigated when the main oscillator was subjected to harmonic and impulse excitations. The slow flow equations of the coupled system were derived by using the complexification?averaging method, and the nonlinear equations which describe the steady?state response were obtained. As the harmonic excitation force increased, the system which comprises constant?stiffness NES generated higher branch responses, greatly reducing the vibration absorption efficiency. The influence of nonlinear stiffness on the responses of the system was investigated. Results show that, with the increase of harmonic exciting force, a reduction of NES stiffness can eliminate the higher branch responses and even the frequency band of strongly modulated responses. The vibration absorption efficiency of variable?stiffness NES attached to the linear oscillator for different amplitudes of impulse excitation was investigated. Results show that the proper reduction of nonlinear stiffness under increasing impulse excitation can greatly increase the vibration absorption efficiency of NES, and the variable?stiffness design can effectively mitigate the negative influences of the increase of the excitation amplitude on the efficiency of constant?stiffness NES.