To evaluate the stability of glasses, a new criterion k(f)(T) = v exp[-E/RT.(T-p - T-f)/T-f] is proposed, where T-f is the inflection point temperature and T,is the maximum peak temperature on the differential thermal analysis curves. Not only the kinetic parameters of the crystallization of glasses, namely, activation energy, E, and frequency factor, v, but also a thermodynamic factor (T, - Ti)/Tf have been taken into account in the k(f)(T) criterion. A higher value of kf(T) means a poor stability of glasses. Two glasses with the compositions of Li2O . 2SiO(2) and Li2O . 1.5SiO(2) were prepared by the conventional melting process and the validity of the proposed criterion is ascertained by applying it on these glasses. The stability of these two glasses was also evaluated by the existing criteria. The results indicate that all existing criteria are either affected by the heating rate or they are not suitable for evaluating the stability of these glasses. On the contrary, the new criterion is independent of the heating rate and gives consistent results on the evaluation of the stability of Li2O-SiO2 glasses within a large temperature range. The Li2O . 1.5SiO(2) glass is less stable than the Li2O . 2SiO(2) glass.