We have proposed a novel approach for studying oscillations with extragalactic neutrinos. Active Galactic Nuclei and Gamma Ray Bursts are believed to be sources of ultrahigh energy muon neutrinos. With distances of 100 Mpc or more, they provide an unusually long baseline for possible detection of with mixing parameters down to eV, many orders of magnitude below the current accelerator experiments. By solving the coupled transport equations, we show that high-energy 's, as they propagate through the earth, cascade down in energy, producing the enhancement of the incoming flux in the low energy region, in contrast to the high-energy 's, which get absorbed. For an AGN quasar model we find the flux to be a factor of to larger than the incoming flux in the energy range between GeV and GeV, while for a GRB fireball model, the enhancement is - in the same energy range and for zero nadir angle. This enhancement decreases with larger nadir angle, thus providing a novel way to search for appearance by measuring the angular dependence of the muons. To illustrate how the cascade effect and the final flux depend on the steepness of the incoming , we show the energy and angular distributions for several generic cases of the incoming tau neutrino flux, for and . We show that for the incoming flux that is not too steep, the signal for the appearance of high-energy is the enhanced production of lower energy and their distinctive angular dependence, due to the contribution from the decay into just below the detector.