Five years after the meeting "Quaternionic Structures in Mathematics and Physics", which took place at the International School for Advanced Studies (SISSA), Trieste, 5-9 September 1994, we felt it was time to have another meeting on the same subject to bring together scientists from both areas. The second Meeting on Quaternionic Structures in Mathematics and Physics was held in Rome, 6-10 September 1999. Like in 1994, also this time the Meeting opened a semester at The Erwin Schrodinger International Institute for Mathematical Physics of Vienna, that in Fall 1999 was dedicated to "Holonomy Groups in Differential Geometry", and many participants of this ESI program were invited speakers at the.