The origin of cosmic rays is one of the most important questions in modern astrophysics. Leading world observatories are engaged in their search in our Galaxy and beyond. Current observations of bright sources of hard X-rays and gamma radiation require precise models of cosmic-ray accelerators and emission generation. Recent detection of astrophysical neutrinos with the energy exceeding 1015 eV achieved by the IceCube Neutrino Observatory and registration by the LOFAR observatory of the light cosmic-ray component at 1016–1017 eV have given rise to a wide discussion of whether its sources are galactic or extragalactic. H.E.S.S. observations of high-energy gamma-ray sources in compact massive clusters Westerlund 1 and Cl*1806-20 triggered a new search for the models of effective accelerators of high-energy cosmic rays, socalled galactic PeVatrons. In this paper, the properties of compact massive young stellar clusters as possible sources of cosmic rays, neutrinos, and gamma emission are discussed. We suppose that an expanding supernova remnant in a compact massive cluster is an effective cosmic-ray accelerator up to the energies of 1015 eV and beyond. Energy spectra of particles being accelerated in the system of colliding shocks generated by a supernova remnant interaction with nearby stellar winds have a broken power-law shape with a strong upturn around several teraelectronvolts and a cutoff energy at tens of petaelectronvolts. These sources provide the maximal emission flux at the maximal energies of the spectrum. Teraelectronvolt sources detected by H.E.S.S. could be related to supernova remnants in Westerlund 1 and Cl*1806-20 and be responsible for the 10% of the IceCube neutrino events. We have also shown that PeVatrons in the systems of colliding shocks can provide up to 80% of the light cosmic-ray component at the energies of 1016–1017 eV detected at the Earth.