  The Dotsenko-Fateev integral is an analytic function of one complex variable
expressing the amplitude in the 4-point correlator of the 2D conformal field
theory. Dotsenko-Fateev found ODE of third order with Fuchsian singularities
satisfied by their integral. In the present paper, this work is extended to
generalized Dotsenko-Fateev integrals, in particular those associated to
arbitrary multipoint correlators, and Pfaff systems of PDE of Fuchsian type are
constructed for them. The ubiquity of the Fuchsian systems is in that they
permit to obtain local expansions of solutions in the neighborhoods of
singularities of the system.
