The reduced magnetic moments of oxide-free FePt nanoparticles are discussed in terms of lattice expansion and local deviation from the averaged composition. By analyses of the extended x-ray absorption fine structure of FePt nanoparticles and bulk material measured both at the Fe K and Pt L(3) absorption edge, the composition within the single nanoparticles is found to be inhomogeneous, i.e. Pt is in a Pt-rich environment and, consequently, Fe is in an Fe-rich environment. The standard Fourier transformation-based analysis is complemented by a wavelet transformation method clearly visualizing the difference in the local composition. The dependence of the magnetic properties, i.e. the element-specific magnetic moments on the composition in chemically disordered Fe(x)Pt(1-x) alloys, is studied by fully relativistic SPR-KKR band structure calculations supported by experimental results determined from the x-ray magnetic circular dichroism of 50 nm thick films and bulk material.