The paper is devoted to the influence of the fourth element on the microstructure of the rapidly-solidified alloys of the Al–Mg–Zr-system. Alloys were additionally doped with high-melting-point metals Ti, Hf, W, and Nb. In the structure of all samples in the immediate area of the cooled surface, uniformly distributed intermetallic inclusions of several nanometers in size were detected. Such a structure can be represented as a dispersion-strengthened composite. A quantitative metallographic analysis was carried out to quantitatively describe the structure of the obtained particles of the cooled melt. The obtained rapidly-solidified alloys can be described as dispersion-strengthened composite materials with the aluminum-magnesium alloy matrix and the intermetallic particles strengthener. Depending on the alloying component, these particles differ in shape (spheres, plates, agglomerates) and in size (from 200 nm when alloying with Hf and W up to 1.2-1.5 μm with Ti and Nb alloying). The X-ray phase analysis (XPA) showed that in the studied alloys of the Al–5Mg–1.2Zr–(0.5÷2.0)X-system, high cooling rates of melts lead to the formation of new intermetallic compounds that are absent in equilibrium systems. The example of an alloy with hafnium additive shows that an increase in the content of the alloying component (from 0.5 to 2 % by mass) leads to an increase in the volume ratio of intermetallic inclusions (from 5 to 12.8 %). At the same time, their shape and average size remain unchanged. The additional alloying component will improve the mechanical characteristics of aluminum alloys by increasing the recrystallization threshold of a rapidly-solidified alloy.