The vibration absorption efficiencies of a singledegreeoffreedom (SDOF) NES and a 2degreeoffreedom (2DOF) series NES were compared,and the suppression of higher branch response by the 2DOF NES was analyzed. The slow flow equations of the system were derived by complexificationaveraging method,and the frequencyresponse curves were obtained. The response of the system attached with the SDOF NES were compared with that of the system with the series NES, under harmonic excitations with different amplitudes. The results show that the series NES can maintain high vibration absorption efficiency in a large range of excitation amplitudes. Furthermore,the parameter influences of the 2DOF series NES on the vibration suppression effect were investigated under two excitation amplitudes. The vibration absorption for the host oscillator is mainly influenced by the primary NES under the smallamplitude excitation, but by the secondary NES under the largeamplitude excitation.