The sensitivity of a large water Čerenkov neutrino telescope in detecting possible oscillations (vμ→vτ) and (vμ→ve) of atmospheric neutrinos is studied, taking also into account the Wolfenstein, Mikheyev and Smirnov matter effects. The large water Čerenkov device is able to detect with high accuracy upward-going muons with energies greater than 10 GeV. After one year running time the search for ν oscillations will reach the following sensitivity for the oscillation parameters: Δm2>3·10−3 (eV2), for sin22θ=1, sin22θ>4·10−2, for Δm2>0.1 (eV2) for the oscillation (vμ→vτ) and δm2>4·10−3 (eV2), for sin22θ=1, sin22θ>8·10−3, for δm2=6·10−2 (eV2) for the oscillation (vμ→ve). These limits are well below the current accelerator and reactor limits. It is also stressed the importance of such a measurement in the context of solar ν puzzle.