  We investigate the nonlinear realization of partially broken $N$=2 global
supersymmetry in the D=2 and 3 anti de-Sitter (AdS) space. We particularly
study Nambu-Goldstone degrees of freedom for the $N$=2 AdS supersymmetry
partially broken down to $N$=1 AdS supersymmetry, where we observe a NG fermion
of the broken supersymmetry and a NG boson of the internal symmetry which form
a NG multiplet. Based on the nonlinear realization method, we construct a
superspace formalism for 2 and 3 dimensional AdS space and evaluate the
covariant derivatives and supervielbeins for the AdS superspace. Finally we
obtain the nonlinear transformation laws and the lowest order of effective
Lagrangians.
