  The dynamics of linear perturbations in a radiatively cooling dusty plasma is
considered, with the charge of both dust ($Z_d$) and plasma ($Z_p$) components
being allowed to vary with their densities. It is shown that in the
long-wavelength limit corresponding to the characteristic cooling length, when
the plasma can be treated as quasineutral, the presence of dust particles
changes the criteria for radiation instability, regardless the charging process
of the dust particles. In particular, the condensation (isobaric) mode is shown
to be stabilized (destabilized) if in the equilibrium, the relation between
densities of the dust $n_d$ and plasma $n$ under the quasineutrality condition,
$(d\ln n_{d}/d \ln n)_{q}<1$ ($>1$) is satisfied, while the isentropic mode is
stabilized (destabilized) when the opposite inequalities take place; the
isochoric mode is unaltered. Numerical estimates show that these effects can be
important in hot phases ($T\sim 10^{6}$ K) of the interstellar plasma, and in
tokamak plasma near the walls.
