ESDU 06011 is the third in a series of Items devoted to fatigue damage under random loading. This Item considers spectral methods for the estimation of fatigue life. It is to be applied in cases where the power spectral density function of stress is known. Several methods are considered. These include: Wirsching and Light@ Chaudhury and Dover@ Dirlik@ Ortiz and Chen@ Larsen and Lutes@ and Zhao and Baker. A program for fatigue life estimation is included. The program is used to estimate the spectral moments of the power spectral density functions of the signal@ the number of peaks per second and the number of upward zero crossings per second in the time series. Fatigue life is estimated@ using the method of Dirlik. Examples illustrating the use of the program are given. The spectral moments of the response of single degree of freedom systems to white noise are described and methods for their estimation are outlined. Other Items in the series are concerned with cycle counting and crack propagation methods for the estimation of fatigue life. The Items in the series are: Fatigue Damage and Life under Random Loading ?C ESDU 06009@ Cycle Counting Methods for the Estimation of Fatigue Life ?C ESDU 06010@ Spectral Methods for the Estimation of Fatigue Life ?C ESDU 06011 (this Item)@ Crack Propagation Methods for the Estimation of Fatigue Life ?C (ESDU 07012).