This paper provides theoretical formulas to calculate conservative estimates of the rainflow fatigue damage from the spectral parameters for spectra composed of the combination of one or several narrow-band low-frequency loads and a higher frequency one, such as are often encountered with moored marine structures. With respect to the semi-empirical formulas that have been proposed by other authors, those presented here are theoretically constructed from the mathematical definition of rainflow and from the statistical properties of Gaussian processes. (C) 2008 Elsevier Ltd. All rights reserved.