It is shown that novel kinds of cosmological structures can arise if t
here are flat (or almost flat) directions of the scalar potential that
intersect each other, as happens in some simple supersymmetric models
. One example is ''diffuse domain walls'' whose energy density is only
of order T-4. It is shown that as the universe expands the scale of t
he domains themselves remains of the order of the horizon scale, while
the energy in the diffuse walls remains a roughly fixed fraction of t
he energy in matter.