  We show that under particular circumstances a general relativistic
spherically symmetric bounded distribution of matter could satisfy a nonlocal
equation of state. This equation relates, at a given point, the components of
the corresponding energy momentum tensor not only as function at that point,
but as a functional throughout the enclosed configuration. We have found that
these types of dynamic bounded matter configurations, with constant
gravitational potentials at the surface, admit a Conformal Killing Vector and
fulfill the energy conditions for anisotropic imperfect fluids. We also present
several analytical and numerical models satisfying these equations of state
which collapse as reasonable radiating anisotropic spheres in general
relativity.
