The low-temperature anomalies of glass forming systems are analyzed fo
cusing on the concept of fragility. It is shown that two extremes on t
he fragility plot, SiO2 and Ca0.4K0.6(NO3)(1.4), show a strong differe
nce in specific heat in the range of excess vibrational contribution.
This difference cannot be explained in the framework of the soft poten
tial model in its present state. A relation between the excess vibrati
onal contribution and the amount of structural fluctuations is suggest
ed. It is shown that the suggested relation explains the found differe
nce in low-temperature specific heat between strong and fragile glass
formers.