  We present the results of a search for high energy extraterrestrial neutrinos
with the Baikal underwater Cherenkov detector NT200, based on data taken in
1998 - 2002 (1038 live days).Upper limits on the diffuse fluxes of
\nu_e+\nu_{\mu}+\nu_{\tau}, predicted by several models of AGN-like neutrino
sources, are derived. For an E^{-2} behavior of the neutrino spectrum, our
limit is E^2 \Phi_{\nu}(E)<8.1 10^{-7} cm^{-2} s^{-1} sr^{-1} GeV over a
neutrino energy range 2 10^4 - 5 10^7 GeV covering 90% of expected events. The
upper limit on the resonant \bar{\nu}_e diffuse flux is \Phi_{\bar{\nu}_e} <
3.3 10^{-20} cm^{-2}s^{-1}sr^{-1}GeV^{-1}.
