  We study the non-selfadjoint Dirac system on a finite interval having
non-integrable regular singularities in interior points with additional
matching conditions at these points. Properties of spectral characteristics are
established, and the inverse spectral problem is investigated. We provide a
constructive procedure for the solution of the inverse problem, and prove its
uniqueness. Moreover, necessary and sufficient conditions for the global
solvability of this nonlinear inverse problem are obtained.
