The polarization-optical and Bitter powder methods were used to study the evolution of the magnetic domain structure in the process of atomic ordering upon the annealing of quenched single-crystal CoPt samples in the presence of an elastic tensile load. It was shown that after a short-term annealing, a magnetic domain structure is formed in the samples that is analogous in its general appearance to the domain structure of magnetically uniaxial crystals. On various scale levels, systems of {110} bands were revealed, which represent elements of a structural hierarchy. They differ in size and contrast (density of powder patterns) and configuration and width of magnetic domains. With increasing annealing time, a correlated change in the dimensions of the elements of the structural hierarchy and parameters of the domain structure occurs. Bending, wavelike, and vortex-like changes in the structural elements were revealed. The results obtained are discussed with allowance for the known concepts of the complex stressed state of crystals and of the nonlinear nonlocal model of the fcc-fct phase transformations.