The comprehensive experimental and theoretical study of the processes of local ordering of multicomponent alloys was carried out. Experimental techniques included atom-probe tomography and measurement of electrical resistivity during isochronal annealing. The theoretical study was carried out by atomistic modeling methods. The evolution of the system was described in the framework of the multiscale paradigm which is based on quantum-mechanical calculations. The initial stage of the decomposition of a solid solution of CoCrFeNi alloy with the formation of Ni4Cr and Ni2Cr precipitations was demonstrated for the first time by the employed approach.