[en] Production spectra of high-energy neutrinos from galactic cosmic ray interactions with interstellar gas and extragalactic ultrahigh energy cosmic-ray interactions with microwave black-body photons are presented and discussed. These production processes involve the decay of charged pions and are thus related to the production of cosmic gamma-rays from the decay of neutral pions. Estimates of the neutrino fluxes from various diffuse cosmic sources are then made and the reasons for significant differences with previous estimates are discussed. Predicted event rates for a DUMAND type detection system are significantly lower than early estimates indicated