  We examine spontaneously broken N=2 supersymmetry in four dimensions and
associate a spinor superfield with each Goldstino via a finite supersymmetry
transformation with parameters that are the Grassmann coordinates of N=2
superspace. Making use of a special choice of coset parametrization allows us
to develop a version of nonlinearly realized N=2 supersymmetry for which the
associated Goldstino superfields are defined on harmonic superspace, thereby
providing a natural mechanism for construction of a Goldstino action. The
corresponding superfield Lagrangian is an O(4) multiplet. This property is used
to reformulate the Goldstino action in projective superspace and in
conventional N=2 superspace. We show how to generate matter couplings of the
Goldstinos to supersymmetric matter using the N=2 harmonic, projective and full
superspaces. As a bi-product of our consideration, we also derive an N=2 chiral
Goldstino action.
