Neutrino fluxes from strong radio sources are estimated, assuming the neutrino-production mechanism: p+p→nucleons+mesons→nucleons+electrons, gamma rays, and neutrinos. The neutrino fluxes calculated on the basis of this mechanism are too small to be easily detected unless there are resonances in neutrino processes associated with the production of intermediate bosons. It is shown that a resonance in the antineutrino-electron system, associated with the usually hypothesized W- resonance, could be used to test, with standard experimental techniques, whether strong radio sources emit high-energy neutrinos in the quantities estimated in this paper. Two kinds of observational tests are described and counting rates are estimated. Observational tests of the kind we propose would provide important information about: (1) the mechanism for production of high-energy electrons in strong radio sources, and (2) the magnetic fields in such sources. Some comments concerning other logically possible neutrino resonances are also included.