E.G.D. Cohen G. Gallavotti Note on Two Theorems in Nonequilibrium Statistical Mechanics (18K, Latex (Revtex)) 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.