  Neutrino telescopes that measure relative fluxes of ultrahigh-energy
$\nu_{e}, \nu_{\mu}, \nu_{\tau}$ can give information about the location and
characteristics of sources, about neutrino mixing, and can test for neutrino
instability and for departures from CPT invariance in the neutrino sector. We
investigate consequences of neutrino mixing for the neutrino flux arriving at
Earth, and consider how terrestrial measurements can characterize distant
sources. We contrast mixtures that arise from neutrino oscillations with those
signaling neutrino decays. We stress the importance of measuring $\nu_{e},
\nu_{\mu}, \nu_{\tau}$ fluxes in neutrino observatories.
