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 F-p+1(p), and the other, AppellF1F4, for manipulations with Appell hypergeometric functions F-1, F-2, F-3, F-4 of two variables. Program summary Program title: HYPERDIRE Catalogue identifier: AEPP\_v1\_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPP\_v1\_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 3428 No. of bytes in distributed program, including test data, etc.: 394247 Distribution format: tar.gz Programming language: Mathematica. Computer: All computers running Mathematica. Operating system: Operating systems running Mathematica. Classification: 4.4. Nature of problem: Reduction of hypergeometric functions F-p(p-1), F-1, F-2, F-3, F-4 to sets of basis functions. Solution method: Differential reduction Running time: Dependent on the complexity of problem. The examples provided take less than a minute to run. (c) 2013 Elsevier B.V. All rights reserved.