We study prospects for the observations of high-energy cosmic tau neutrinos (E ≥ 10 6 GeV) originating from proton acceleration in the cores of active galactic nuclei. We consider the possibility that vacuum flavor neutrino oscillations induce a tau to muon neutrino flux ratio greatly exceeding the rather small value expected from intrinsic production. The criterias and event rates for under water/ice lightČerenkov neutrino telescopes are given by considering the possible detection of downgoing high-energy cosmic tau neutrinos through characteristic double shower events. PACS number(s): 95.55. Vj, 14.60.Pq, 13.15.+g, 98.54.Cm