AbstractThe influence of stochastic velocity fields with finite correlation lengths on the formation of spectral lines is taken into account without restrictions to specific velocity models. To construct a perturbation theory treating the influence of stochastic motion on the radiative transfer we start with the stochastic transfer equation for plane‐parallel atmospheres and expand it to an infinite hierarchical system. An appropriate cut‐off of the infinite system admits to achieve exactly the micro‐ and macroturbulent limit at every level of approach. The formalism is derived forn‐point correlations of the absorption coefficient and specialised for 2‐point cor