Context. The Magellanic Clouds, two dwarf galaxy companions to the Milky Way, are among the Fermi Large Area Telescope (LAT) brightest γ-ray sources. Aims. We present comprehensive modeling of the non-thermal electromagnetic and neutrino emission in both Clouds. Methods. We self-consistently model the radio and γ-ray spectral energy distribution from their disks based on recently published Murchison Widefield Array and Fermi/LAT data. All relevant radiative processes involving relativistic and

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... hermal electrons (synchrotron, Compton scattering, and bremsstrahlung) and relativistic protons (neutral pion decay following interaction with thermal protons) are considered, using exact emission formulae. Results. Joint spectral analyses indicate that radio emission in the Clouds has both primary and secondary electron synchrotron and thermal bremsstrahlung origin, whereas γ rays originate mostly from π 0 decay with some contributions from relativistic bremsstrahlung and Comptonized starlight. The proton spectra in both galaxies are modeled as power laws in energy with similar spectral indices, ∼2.4, and energy densities, ∼1 eV cm −3 . The predicted 0.1-10 GeV neutrino flux is too low for detection by current and upcoming experiments. Conclusions. We confirm earlier suggestions of a largely hadronic origin of the γ-ray emission in both Magellanic Clouds.