  Correlations of eigenfunctions,
$\langle|\psi_k(r_1)|^2|\psi_l(r_2)|^2\rangle$, in a disordered system are
investigated. We derive general formulae expressing these correlation functions
in terms of the supermatrix sigma-model. In particular case of weak
localization regime we find that the correlations of the same eigenfunction are
proportional to $g^{-1}$ for large distances, while the correlations of two
different eigenfunctions cross over from $g^{-1}$ behavior for $r_1=r_2$ to
$g^{-2}$ one for $\vert r_1 - r_2 \vert \gg l$, with $g$ and $l$ being the
dimensionless conductance and the mean free path, respectively.
