  The stability properties of one-dimensional radiative shocks with a power-law
cooling function of the form $\Lambda \propto \rho^2T^\alpha$ are the main
subject of this work. The linear analysis originally presented by Chevalier &
Imamura, is thoroughfully reviewed for several values of the cooling index
$\alpha$ and higher overtone modes. Consistently with previous results, it is
shown that the spectrum of the linear operator consists in a series of modes
with increasing oscillation frequency. For each mode a critical value of the
cooling index, $\alpha_\textrm{c}$, can be defined so that modes with $\alpha <
\alpha_\textrm{c}$ are unstable, while modes with $\alpha > \alpha_\textrm{c}$
are stable. The perturbative analysis is complemented by several numerical
simulations to follow the time-dependent evolution of the system for different
values of $\alpha$. Particular attention is given to the comparison between
numerical and analytical results (during the early phases of the evolution) and
to the role played by different boundary conditions. It is shown that an
appropriate treatment of the lower boundary yields results that closely follow
the predicted linear behavior. During the nonlinear regime, the shock
oscillations saturate at a finite amplitude and tend to a quasi-periodic cycle.
The modes of oscillations during this phase do not necessarily coincide with
those predicted by linear theory, but may be accounted for by mode-mode
coupling.
