The inherently nonlinear phenomenon of fatigue crack propagation is modeled as a linear random process. To a first approximation, simple, nonstationary time series models are introduced and standard techniques for determining the parameters of autoregressive integrated moving-average processes are applied. Multiplicative time series models are next utilised for the representation of a group of crack history curves. Implementation of the models on the Virkler experimental data set yields satisfactory results. Reliable Gaussian approximations to the distribution of the time required by a crack to reach a specified critical length are obtained, and the usefulness of the approach is demonstrated when updating lifetime predictions after periodic inspections.