We propose a double exchange model to describe the RuO2 planes of RuSr2(Eu,Gd)Cu2O8. The Ru +5 ions are described by localized spins, and additional electrons provided by the superconducting CuO2 planes are coupled ferromagnetically to them by Hund rules coupling. We calculate the spin structure factor, magnetic susceptibility and magnetization as a function of magnetic field and temperature, using a Monte Carlo algorithm in which the Ru +5 spins are treated as classical. Several experiments which seemed in contradiction with one another are explained by the theory.PACS numbers: 75.30. Vn, 75.40.Mg RuSr 2 (Eu,Gd)Cu 2 O 8 is a very interesting material because of the coexistence of magnetic order and superconductivity below T S ∼ 45 K. 1,2 The system orders magnetically at T M = 133 K, but the type of magnetic order remains controversial. The first measurements in Gd samples indicated ferromagnetic (FM) ordering of the Ru moments, 1 but neutron diffraction experiments found superlattice reflections consistent with an antiferromagnetic (AF) order with nearest-neighbor spins antiparallel in all three directions. 3 The Ru contribution to the magnetic susceptibility at temperature T > T M can be very well described by χ = C/(T − Θ), with Θ = 100 ± 3 K. 4 The fact that Θ > 0 seems difficult to reconcile with AF order at low temperatures.From previous intensive research on the similar system YBa 2 Cu 3 O 6+x , 5 it seems clear that each of the superconducting CuO 2 planes has doping slightly less than 0.1 holes per Cu ion in order to lead to the observed superconducting critical temperature T S . Since Eu or Gd are expected to be in the oxidation state +3, assuming as usual that the inactive SrO layers are neutral, charge balance imposes that the RuO 2 planes have an electron doping n 0.2 per Ru ion. 5 Neglecting covalency with O atoms, this means that there are 1 − n Ru +5 and n Ru +4 ions per unit cell. The superconducting CuO 2 planes and the magnetic RuO 2 planes can be regarded as separate entities as a first approximation. This is supported by symmetry considerations and band-structure calculations. 6 We propose that the electronic structure of the RuO 2 planes can be described by an effective double exchange model, with one localized spin at each site representing the Ru +5 ions, and additional n itinerant electrons per Ru coupled ferromagnetically with the localized spins.The model is the two-dimensional (2D) version of one widely used in manganites:Here S i is the localized spin operator representing the Ru +5 ion at site i, c † iσ is the operator creating an itinerant electron of spin σ at this site, and s i = αβ c † iα σ αβ c iβ gives the spin of this electron. For simplicity we take the Hund coupling, J H → +∞.The model is solved using a classical Monte Carlo (MC) procedure for the localized spins, in conjunction with exact diagonalization of the conduction electron system. 7 The localized spins are taken to be classical and of magnitude one. The conduction electrons are assumed to occupy a single orbita...