  We have investigated time evolutions of power spectra of density fluctuations
for long time after the first appearance of caustics in the expanding
one-dimensional universe. It is found that when an initial power spectrum is
sale-free with a power index $n$, a self-similarity of the time evolution of
the power spectrum is achieved. We find that the power spectrum can be
separated roughly into three regimes according to the shape of the power
spectrum: the linear regime ($k < k_{nl}$ : the regime {\cal 1}),the
single-caustic regime($k_{nl} < k < k_{snl}$ : the regime 2), and the
multi-caustics regime($k > k_{snl}$ : the regime 3). The power index of the
power spectrum in each regime has the values of $n,-1$, and $\mu$ which depends
on $n$, respectively. Even in the case of an initial power-law spectrum with a
cutoff scale, there might be the possibility of the self-similar evolution of
the power spectrum after the appearance of the caustics. It is found, however,
the self-similarity is not achieved in this case. The shape of the power
spectrum on scales smaller than the cutoff scale can be separated roughly in
two regimes: the virialized regime ($k_{cut}< k < k_{cs}$ : the regime 4), and
the smallest-single-caustic regime ($ k > k_{cs}$
  : the regime 5). The power index of the power spectrum is $\nu$ which may be
determined by the distribution of singular points in the regime 4. In the
regime 5, the value of the power index is -1. Moreover we show the general
property about the shape of a power spectrum with a general initial condition.
