  An effect generated by the nonexponential behavior of the survival amplitude
of an unstable state at the long time region is considered. It is known that
this amplitude tends to zero as $t$ goes to the infinity more slowly than any
exponential function of $t$. Using methods of asymptotic analysis we find the
asymptotic form of this amplitude in the long time region in a general model
independent case. We find that the long time behavior of this amplitude affects
the form of the energy of unstable states: This energy should be much smaller
for suitably long times $t$ than the energy of this state for $t$ of the order
of the lifetime of the considered unstable state.
