  We study the approximate analytical solutions of the Dirac equation for the
generalized Woods-Saxon potential with the pseudo-centrifugal term. In the
framework of the spin and pseudospin symmetry concept, the approximately
analytical bound state energy eigenvalues and the corresponding upper- and
lower-spinor components of the two Dirac particles are obtained, in closed
form, by means of the Nikiforov-Uvarov method which is based on solving the
second-order linear differential equation by reducing it to a generalized
equation of hypergeometric type. The special cases $\kappa =\pm 1$ ($l=%
\widetilde{l}=0,$ s-wave) and the non-relativistic limit can be reached easily
and directly for the generalized and standard Woods-Saxon potentials. Also, the
non-relativistic results are compared with the other works.
