In this work the influence of alloy composition and heat treatment conditions of Al-Y and Al-Y-Ni glasses on size, morphology and composition of crystals created during the first stage of crystallization of the alloys was studied. Amorphous ribbons of Al90Y10 and Al80Y5Ni15 were prepared in air by the single-roller melt-spinning method. Partial crystallization of the ribbons was obtained by continous heating to the temperature of the first calorimetric peak applying slow (2K/min) and fast (200K/min) heating. The structure of partially crystallized alloys was investigated using X-ray Diffractometry and Transmission Electron Microscopy. It was found that the first stage of crystallization of the glasses studied depended on alloy composition. Primary and eutectic crystallization was found in the Al90Y10 and the Al80Y5Ni15 glass, respectively. A strong influence of heat treatment conditions on the structure of the Al80Y5Ni15 alloy and the lattice parameter of Al-based solid solutions in the ternary as well as in the binary alloy was observed.