HYPERDIRE, HYPERgeometric functions DIfferential REduction: MATHEMATICA-based packages for differential reduction of generalized hypergeometric functions pFp−1,F1,F2,F3,F4. HYPERDIRE is a project devoted to the creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions p+1Fpp+1Fp, and the other, AppellF1F4, for manipulations with Appell hypergeometric functions F1,F2,F3,F4F1,F2,F3,F4 of two variables.