  Linear dynamical systems, driven by a non-white noise which has the Levy
distribution, are analysed. Noise is modelled by a specific stochastic process
which is defined by the Langevin equation with a linear force and the Levy
distributed symmetric white noise. Correlation properties of the process are
discussed. The Fokker-Planck equation driven by that noise is solved.
Distributions have the Levy shape and their width, for a given time, is smaller
than for processes in the white noise limit. Applicability of the adiabatic
approximation in the case of the linear force is discussed.
