A gamma-ray burst fireball is likely to contain an admixture of neutrons, in addition to protons, in essentially all progenitor scenarios. Inelastic collisions between differentially streaming protons and neutrons in the fireball produce muon neutrinos (antineutrinos) of ~ 10 GeV as well as electron neutrinos (antineutrinos) of ~ 5 GeV, which could produce ~ 7 events/year in kilometer cube detectors, if the neutron abundance is comparable to that of protons. Photons of ~ 10 GeV from pi-zero decay and ~ 100 MeV electron antineutrinos from neutron decay are also produced, but will be difficult to detect. Photons with energies < 1 MeV from shocks following neutron decay produce a characteristic signal which may be distinguishable from the proton-related MeV photons.