The method is described for calculating structural relaxation in glasses cooled very rapidly. The major obstacle for the calculation was the assumption in the original model of Arrhenius behavior for the equilibrium viscosity. In this paper the Macedo-Litovitz' hybrid equation is used for the equilibrium viscosity. The glass transition region is shown to shift to higher temperatures and to broaden as the cooling rate increases. Glasses with higher Tg e.g. SiO2 are shown to have broader glass transition region than glasses with lower Tg but similar activation energy.