Dissipative singular Dirac operators are studied in the space L-A(2) ([a,b) ; C-2) (-infinity < a < b less than or equal to infinity), that the extensions of a minimal symmetric operator in Weyl's limit-point case. We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and specify its characteristic function in terms of the Titchmarsh-Weyl function of selfadjoint operator. We prove theorems on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operators. (C) 2003 Elsevier Inc. All rights reserved.