The article reveals for the first time the features of nanoparticle morphology, phase compositions, and their changes when heating FePt and CoPt nanoalloys. Nanoparticles were obtained by co-reduction of precursor solution mixtures with hydrazine hydrate. The features were found by a complex of methods of X-ray diffraction (in situ XRD and X-ray scattering), TEM HR, and cyclic voltammetry. In addition, adsorbometry results were obtained, and the stability of different nanocluster structures was calculated by the molecular dynamics method. There were only FCC solid solutions in the X-ray patterns of the FePt and CoPt nanoalloys. According to XRD, in the case of nanoparticle synthesis with Fe and Co content less than 10 at. %, the composition of solid solutions was close to or practically equal to the composition of the as-synthesized nanoparticles quantified by inductively coupled plasma optical emission spectrometry. For systems synthesis with Fe and Co content greater than the above, the solubility limits (SLs) of Fe and Co in Pt were set 11.4 ± 0.7 at. % and 17.5 ± 0.6 at. %, respectively. Therefore, there were non-registered XRD extra-phases (XRNDPh-1) in the systems when CFe,Co ≥ SL. This statement was supported by the results of TEM HR and X-ray scattering: the smallest nanocrystals (1–2 nm) and amorphous particles were found, which qualitatively agreed with the sorbometry and SAXS results. Molecular dynamics calculations of stability for FePt and CoPt alloys claimed the structures of the most stable phase corresponded to phase diagrams (A1 and L12). Specific peculiarities of the morphology and compositions of the solid solutions of nanoalloys were established: structural blockiness (domain) and composition heterogeneity, namely, platinum enrichment of internal (deep) layers and homogenization of the nanoalloy compositions at relatively low temperatures (130–200 °C). The suggested model of the formation of nanoalloys during the synthesis, qualitatively, was compliant with the results of electrochemical deposition of FePt films on the surface of various electrodes. When nanocrystals of solid solutions (C(Fe, Co) < SL) were heated above specific temperatures, there were phase transformations with the formation of two-phase regions, with solid solutions enriched with platinum or iron (non-registered XRD phase XRNDPh-2). The newly formed phase was most likely intermetallic compounds, FePt3, CoPt3. As a result of the study, the model was developed, taking into account the nanoscale of the particles: XRDPh (A1, FeaPt1−a) → XRDPh (A1, Fem×a−xPtm−m×a+x) + XRNDPh-2 (Fen×a+yPtn−n×a−y) (here, m + n = 1, m ≤ 1, n ≤ 1).