The fructose/water phase diagram is determined by conventional DSC. No hydrates are observed and vitrification is achieved at 40 K/min on cooling for concentrations >55%w/w. The Couchman model, the Gordon model and the Jenckel-Heusch model are tested for the compositional variation of the fictive glass-transition temperature. The data at all these models, except the last, and predict a specific heat change at the glass transition for pure water of 18.9+/-1.5 and 13.5/-+0.8 cal/ (K mol), respectively, for the first and second models. The fictive glass-transition temperature, T-f, is determined as a function of cooling rate V. The associated activation energy d(ln (V)/d(1/T-f) is somewhat constant before increasing as the concentration increases above the limiting glass concentration. This concentration is found to be 78 wt%, defining the temperature T-g' at -57 degrees C for fructose. The change of specific heat at the glass transition presents a minimum for the wholly vitrified samples for a stronger thermodynamic grassy state for concentrations between 80 to 95%wt/wt as the kinetic approach, using the fragility factor, leads to a stronger kinetic glassy state close to 75%wt/wt corresponding to T-g'.