A solution of a random copolymer showing polydispersity only with respect to chemical composition is considered. A model distribution very flexible in its breadth and in its asymmetry is used to describe the polydispersity. Based on continuous thermodynamics, equations for the cloud-point curve, the shadow curve, the spinodal, the critical point, and the heterogeneous double critical point are derived. the activity coefficients are calculated with the aid of Huggins' χ-parameter concept assuming χ to depend linearly on the average chemical composition of the copolymer. the influence of the breadth and the asymmetry of the distribution on the liquid-liquid equilibrium of the copolymer solution is discussed.