  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. 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 an
neutrino energy range $2 10^4 - 5 10^7 GeV$. The upper limit on the resonant
$\bar{\nu}_e$ diffuse flux is $\Phi_{\bar{\nu}_e}< 3.3 10^{-20} cm^{-2} s^{-1}
sr^{-1} GeV^{-1}$.
