Linear dynamical systems, driven by a non-white noise which has the Lévy distribution, are analysed.Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Lévy distributed symmetric white noise.Correlation properties of the process are discussed.The Fokker-Planck equation driven by that noise is solved.Distributions have the Lévy 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.