In zero magnetic field, the magnetic system of a Dy/Y multilayer superstructure represents a spin spiral with a coherence length many times exceeding the Y/Dy bilayer thickness. When the magnetic spiral period does not coincide with the Dy-layer thickness, each structural layer is characterized by an average uncompensated magnetic moment. In an applied magnetic field, magnetic layers tend to order ferromagnetically. Along with ferromagnetic order coaxial to the magnetic field, fourfold commensurate spin structure similar to a spiral and twofold commensurate spin structure similar to antiferromagnetic spin-flop ordering are formed. The fourfold structure is observed at temperatures close to the critical Néel temperature at d_S > d_Dy (T_N = 160 K) in relatively weak magnetic fields. The twofold structure of an antiferromagnet is characteristic of relatively strong fields. This phenomenon is explained in terms of the competition between the Ruderman–Kittel–Kasuya–Yoshida and Zeeman interactions.