Generalising the standard frailty models of survival analysis, we propose to model frailty as a weighted Lévy process. Hence the frailty of an individual is not a given quantity, but develops over time. Formulae for the population hazard and survival functions are derived. The power variance function Lévy process is a prominent example. In many cases, notably for compound Poisson processes, quasi-stationary distributions of survivors may arise. Quasi-stationarity implies limiting population hazard rates that are constant, in spite of the continual increase of the individuald hazard. A brief discusion is given of the biological relevance of this finding.