  The stability of a class of electrically charged fluid spheres under radial
perturbations is studied. Among these spheres there are regular stars,
overcharged tension stars, regular black holes, quasiblack holes, and
quasinonblack holes, all of which have a Reissner-Nordstr\"om exterior. We
formulate the dynamical perturbed equations by following the Chandrasekhar
approach and investigate the stability against radial perturbations through
numerical methods. It is found that (i) under certain conditions that depend on
the adiabatic index of the radial perturbation, there are stable charged stars
and stable tension stars; (ii) also depending on the adiabatic index there are
stable regular black holes; (iii) quasiblack hole configurations formed by,
e.g., charging regular pressure stars or by discharging regular tension stars,
can be stable against radial perturbations for reasonable values of the
adiabatic index; (iv) quasinonblack holes are unstable against radial
perturbations.
