  We study the central extensions of the N=1 superalgebras relevant to the
soliton solutions with the axial geometry - strings, wall junctions, etc. A
general expression valid in any four-dimensional gauge theory is obtained. We
prove that the only gauge theory admitting BPS strings at weak coupling is
supersymmetric electrodynamics with the Fayet-Iliopoulos term. The problem of
ambiguity of the (1/2,1/2) central charge in the generalized Wess-Zumino models
and gauge theories with matter is addressed and solved. A possibility of
existence of the BPS strings at strong coupling in N=2 theories is discussed. A
representation of different strings within the brane picture is presented.
