The incommensurate composite systems M14Cu24O41 (M=Ca,Sr,La) are based on two fundamental structural units: CuO2 chains and Cu2O3 ladders. We present electronic structure calculations within density functional theory in order to address the interrelations between chains and ladders. The calculations account for the details of the crystal structure by means of a unit cell comprising 10 chain and 7 ladder units. It turns out that chains and ladders can be treated independently, which allows us to introduce a model system based on a reduced unit cell. For the CuO2 chains, we find two characteristic bands at the Fermi energy. Tight binding fits yield nearest and next-nearest neighbour interactions of the same order of magnitude. PACS numbers: 71.10.Pm: Fermions in reduced dimensions, 71.20.-b: Electron density of states and band structure of crystalline solids, 74.72.-h: Cuprate superconductors Keywords:The isostructural spin-chain compounds M 14 Cu 24 O 41 (M=Ca,Sr,La) have been subject of intensive research in recent years, mainly due to their rich phase diagram and close relations to the high-T c cuprates. Their incommensurate crystal structures consist of planes of quasi one-dimensional CuO 2 chains stacked alternately with planes of two-leg Cu 2 O 3 ladders. The orientation of these chains and ladders defines the crystallographical c-axis, where the lattice constants of the two subsystems satisfy in a good approximation 10c chain ≈ 7c ladder [1,2]. The copper ions are intrinsically hole doped with nominal Cu valence +2.25 for both the Ca and the Sr compound. However, the ladders contain less holes than the chains. The resulting Cu valence of +2.75 for the chain sites corresponds to a quarter filled one-dimensional band [3]. Optical conductivity as well as x-ray absorption experiments suggest that substitution of Ca for Sr induces a transfer of holes from the chains back to the ladders [4]. On La substitution the intrinsic doping decreases, reaching the undoped state with nominal Cu valence +2.00 for La 6 Ca 8 Cu 24 O 41 .In the case of Sr 14 Cu 24 O 41 the CuO 2 chains are non-magnetic with a spin gap of about 130 K [5] and the Cu 2 O 3 ladders show a charge density wave in a wide temperature range [6,7]. In contrast, for Ca rich samples antiferromagnetic ordering is found in the chains [8,9] and the ladders become superconducting under pressure [10]. This strong doping dependence of both the charge and the magnetic order [11,12,13,14] is accompanied by only minor modifications of the crystal structure [15,16,17]. From the theoretical point of view, the magnetic properties of undoped two-leg S=1/2 ladders have been analyzed be means of a Heisenberg model including cyclic ring exchange [18]. Possible effects of hole doping are investigated in [19]. A large spin gap makes the Cu 2 O 3 ladder planes magnetically inert. On the other hand, the magnetic phase diagram of the CuO 2 chains is quite complicated. Ferromagnetism, as expected for Cu-O-Cu bond angles of approximately 90 • in the chains, is realized in La rich...