  Powerspaces of directed spaces play an important role in modeling the
semantics of nondeterministic functional programming languages. The notions of
upper,lower and convex powerspace of a directed space are defined by the way of
free algebras[25]. In this paper, We study the continuity of power structures
of directed spaces and show that the directed lower powerspaces, directed upper
powerspaces and directed convex powerspaces of continuous spaces are continuous
spaces.
