  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
($\nu_e+\tilde{\nu_e}$) diffuse flux of $E^2 \Phi_{\nu}(E)<(1.3 \div 1.9)\cdot
10^{-6} {cm}^{-2} {s}^{-1} {sr}^{-1} {GeV}$ 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
$(\nu_e+\tilde{\nu_e}):(\nu_{\mu}+\tilde{\nu_{\mu}})$=1:2.
