  We study peculiarities of realization of N=2 supersymmetry in N=2 abelian
gauge theory with two sorts of FI terms, electric and magnetic ones, within
manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic
prepotentials. We obtain a `magnetic', duality- transformed superfield form of
the N=2 Maxwell effective holomorphic action with standard electric $FI$ term
and demonstrate that in such a system off-shell N=2 supersymmetry is inevitably
realized in an unusual Goldstone mode corresponding to the {\it partial}
spontaneous breaking down to N=1. On shell, the standard total breaking occurs.
In a system with the two sorts of FI terms, off-shell N=2 supersymmetry is
realized in the partial breaking mode both in the electric and magnetic
representations. This regime is retained on shell due to the Antoniadis-
Partouche-Taylor mechanism. We show that the off-shell algebra of N=2
supersymmetry in the partial breaking realization is modified on gauge-variant
objects like potentials and prepotentials. The closure of spinor charges
involves some special gauge transformations before any gauge-fixing.
