  The (4,4) null superstring equations of motions and constraints on de Sitter
space are given by using the harmonic superspace. These are solved explicitly
by performing a perturbative expansion of the (4,4) superstring coordinates in
powers of c2, the world-sheet speed of light. The analytic expressions of the
zeroth and first order solutions are determined. On the other hand, we study
the quantization of the (4,4)null superstring in de Sitter space and we
describe its superalgebra.
