In the category of stable dcpo's, free constructions w.r.t. algebraic
theories exist. From this, we obtain various stable power domain const
ructions. After handling their properties in general, we concentrate o
n the stable Plotkin power construction. For continuous ground domains
, it is explicitly described in terms of saturated compact sets. In ca
se of algebraic ground domains, this description is isomorphic to Bune
man's lossless power domains.