  We investigate the spin and pseudospin symmetry in the single-particle
resonant states by solving the Dirac equation containing a Woods-Saxon
potential with Green's function method. Taking double-magic nucleus $^{208}$Pb
as an example, three spin doublets $3d$, $2h$, and $1j$ and three pseudospin
doublets $3\tilde{p}$, $1\tilde{i}$, and $1\tilde{j}$ are obtained for the
single-neutron resonant states. By analyzing the energy splittings, we find
that the threshold effect plays an important role in resonant pseudospin
doubles. Besides, there is a reversed level structure of pseudospin doublets in
the continuum. Differently, all the width splittings of either the spin
doublets or the pseudospin doublets are systematically positive and the
splittings are very small except $1\tilde{j}$ doublet. Further studies show
that the splittings of the energies and widths for the resonant (pseudo)spin
doublets are independent. Besides, the similarity properties of the wave
functions of the spin and pseudospin doublets still maintain well in resonant
states.
