  The spatial structure of wave functions of anomalously localized states (ALS)
in disordered conductors is studied in the framework of the $\sigma$--model
approach. These states are responsible for slowly decaying tails of various
distribution functions. In the quasi-one-dimensional case, properties of ALS
governing the asymptotic form of the distribution of eigenfunction amplitudes
are investigated with the use of the transfer matrix method, which yields an
exact solution to the problem. Comparison of the results with those obtained in
the saddle-point approximation to the problem shows that the saddle-point
configuration correctly describes the smoothed intensity of an ALS. On this
basis, the properties of ALS in higher spatial dimensions are considered. We
study also the ALS responsible for the asymptotic behavior of distribution
functions of other quantities, such as relaxation time, local and global
density of state. It is found that the structure of an ALS may be different,
depending on the specific quantity, for which it constitutes an optimal
fluctuation. Relations between various procedures of selection of ALS, and
between asymptotics of corresponding distribution functions, are discussed.
