  We construct low-energy Goldstone superfield actions describing various
patterns of the partial spontaneous breakdown of two-dimensional N=(1,1),
N=(2,0) and N=(2,2) supersymmetries, with the main focus on the last case.
These nonlinear actions admit a representation in the superspace of the
unbroken supersymmetry as well as in a superspace of the full supersymmetry.
The natural setup for implementing the partial breaking in a self-consistent
way is provided by the appropriate central extensions of D=2 supersymmetries,
with the central charges generating shift symmetries on the Goldstone
superfields. The Goldstone superfield actions can be interpreted as manifestly
world-sheet supersymmetric actions in the static gauge of some superstrings and
D1-branes in D=3 and D=4 Minkowski spaces. As an essentially new example, we
elaborate on the action representing the 1/4 partial breaking pattern N=(2,2)
-> N=(1,0).
