We present the results of a search for high energy neutrinos with the Baikal underwater Cherenkov detector {it NT-200.} An upper limit on the ($ u_e+tilde{ u_e}$) diffuse flux of $E^2 Phi_{ u}(E)<(1.3 div 1.9)cdot 10^{-6} {cm}^{-2} {s}^{-1} {sr}^{-1} {GeV}$ within a neutrino energy range $10^4 div 10^7 {GeV}$ is obtained, assuming an $E^{-2}$ behaviour of the neutrino spectrum and flavor ratio $( u_e+tilde{ u_e}):( u_{mu}+tilde{ u_{mu}})$=1:2.
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