We study collective spin excitations in two-dimensional diluted magnetic semiconductors, placed into external magnetic field. Two coupled modes of the spin waves (the electron and ion modes) are found to exist in the system along with a number of the ion spin excitations decoupled from the electron system. We calculate analytically the spectrum of the waves taking into account the exchange interaction of itinerant electrons both with each other and with electrons localized on the magnetic ions. The interplay of these interactions leads to a number of intriguing phenomena including tunable anticrossing of the modes and a field-induced change in a sign of the group velocity of the ion mode.PACS numbers: 75.30. Ds, 76.50.+g Diluted magnetic semiconductors (DMS) have recently been the subject of great interest [1,2] due to their potential in combining magnetic and semiconductor properties in a single material. The DMS are formed by replacing of cations in ordinary semiconductors with magnetic ions, typically Mn ions. Strong exchange interaction between the itinerant electrons and the electrons localized on d-shells of the magnetic ions leads to a number of remarkable features of the DMS. In particular, it results in the effective indirect interaction between the ion spins thus promising for creating room-temperature ferromagnetic systems that may offer advantages of semiconductors. It also dramatically enhances the effective coupling of the itinerant electrons with the external magnetic field. In contrast to conventional GaAs/GaAlAs systems, where small values of g−factor prevents manipulation of the spin degree of freedom, the giant electron Zeeman splitting arising in the DMS as a manifestation of the exchange interaction can be on the order of the Fermi energy [3,4], offering a wide range of spintronics applications.Here we discuss spin excitations in the twodimensional DMS. Our studies are motivated by recent experiments [5][6][7] and a theoretical discussion [7][8][9] focused on the spin dynamics in diluted magnetic Cd 1−x Mn x Te quantum wells placed into the magnetic field [10]. In Ref. 5, the spectrum of the spin waves, ω(k), was measured. Only one excitation mode was observed. It was demonstrated that the excitations exist in a finite range of wavelengths, k < k m , and their group velocity is negative: dω(k)/dk < 0. The experimental data were interpreted [5,8] in terms of conventional spin waves in the Fermi liquids [11], while k m was attributed to the edge of the Stoner continuum of the single-particle spin excitations. Such interpretation implies that the only effect of the magnetic ions on the electron spin waves is the strong renormalization of the electron Zeeman splitting. However, more recent experimental observations [6,7] supported by theoretical studies [7,9] appear to be in disagreement with this conclusion. Indeed, in Refs. [6,7] two modes of the collective homogeneous (k = 0) spin excitations were observed in Cd 1−x Mn x Te wells. The modes were identified [6,7,9] as the spin excitations o...