Long-lived quasilocalized (resonant) electronic states are predicted t
o lie above the mobility edge of a disordered system. A modification o
f the optimum fluctuation method is developed to estimate the density
of such states. It is shown that the density of states tails exponenti
ally with energy above the mobility edge and that this tail is almost
symmetric to the tail of localized states with respect to the mobility
edge. Possible manifestations of the predicted states are discussed.