Recewed December 1981; revised January 1984, accepted March, 1984. Research leading to the DAFNE package was supported in part by the Italian Ministero della Pubblica Istruzlone, under contract T.V. 31.8.33 n.1592/1980 cap. 8551. Authors' addresses: F. Aiuffi-Pentini, Istituto di Matematica Applicata, Universitb di Bari, 70125 Bari, Italy; V. Parisi, Istituto di Fisica "G. Marconi," Universitfi di Roma, 00185 Rome, Italy; F. Zirilli, Istituto Matematico, Universitfi di Camermo, 62032 Camerino (MC), Italy. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1984 ACM 0098-3500/84/0900-0317 $00.75 ACM Transactions on Mathematical Software, Vol. 10, No. 3, September 1984, Pages 317-324.