Structural changes of rapidly cooled ribbons of the amorphous alloys Al88–86(Ni,Co,Fe)6–8(Y,Gd,Nd,La)5–6, which occur during heating at a rate of 10 K/min and lead to a loss of ductility, have been investigated experimentally. It has been shown that samples of the studied alloys are divided into two groups, in the first of which the loss of ductility is due to the formation of a nanocomposite structure, whereas the embrittlement of samples in the second group is caused by processes of structural relaxation in the amorphous phase (decrease in the concentration of a free volume). It has been established for the first time that there is an empirical correlation between the dynamic temperature, after heating to which the alloys lose their ductility at room temperature, and the ratio of the shear modulus to the elastic modulus of the alloys, which is calculated from the nominal chemical composition.