In concentrated glucose glasses with water contents between 10 and 30 wt %, an indication for a transition in mobility of the sugar protons above the glass transition temperature is observed, using proton magnetic resonance techniques. The first transition in mobility is positioned at the glass transition temperature while the second is about 20-30 degrees C higher. The temperature of this second transition is found to depend on water content, resulting in a new line in the state diagram of glucose-water mixtures. In freeze-concentrated glucose glasses we find two similar transitions. We interpret the second transition as the so-called crossover temperature, where the dynamics changes from solid-like to liquid-like. In freeze-concentrated glasses an increase in the amount of ice melting per degree is observed just above the temperature of the second transition. We propose that both in concentrated and freeze-concentrated glucose glasses, this second transition relates to so-called collapse phenomena in glasses.