The stability of the bound excited states of both the hydrogen and hel
ium anions in an environment represented by the statically screened Co
ulomb potential have been studied. Energies have been calculated at th
e full configuration interaction level of theory, as a function of the
screening parameter. Our calculations demonstrate that the bound exci
ted states of both H- and He- survive only under mild screening condit
ions. Stronger screening will yield a sequential electron detachment p
rocess. Finally, the applicability of the present calculations to mode
l real plasmas is discussed.