FM 99-2 Authors: E.G.D. Cohen, G. Gallavotti Title: Note on Two Theorems in Nonequilibrium Statistical Mechanics Abstract: An attempt is made to clarify the difference between a theorem derived by Evans and Searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state. Keywords: Chaos, chaotic hypothesis, large deviations, fluctuations, time reversal E.G.D.C.: The Rockefeller University, New York, NY 10021, USA G.G.: Fisica, Universita' di Roma La Sapienza, P.le Moro 2, 00185, Roma, Italia. tel. +1-212-327-8855, fax +1-212-327-8507 (EGDC) tel. +39-6-49914370, fax +39-6-4957697 (GG) e-mail egdc@rock08.rockefeller.edu, giovanni@ipparco.roma1.infn.it