A family of stochastic models which may be relevant to meteorology is described. The family can be characterized by the intensity of dependence, the heaviness of the probability tails, and the degree of nonlinearity. Two processes, the fractional stable motion and the spectral fractional stable motion, are introduced in some detail, and the range of values of their parameters is investigated. Both processes have scaling properties and display long-range dependence and high variability. ¿American Geophysical Union 1987