Relaxation enthalpies in the vicinity of glass transitions were recorded on the basis of the heat capacity curves measured in nine glass-forming molecular liquids and solutions in the well defined cooling and subsequent heating cycles. It is observed that enthalpy hysteresis in the cooling/heating cycles is less significant in liquids with increasing fragility. A notable correlation of the fragility index m with relaxation enthalpy Delta H-R, glass transition temperature, and heat capacity jump from glasses to liquids is demonstrated. The introduction of Delta H-R favors the thermodynamic evaluation of fragility in the glass forming multicomponent systems such as solutions and alloys.