  We derive eigenvalue asymptotics for Sturm--Liouville operators with singular
complex-valued potentials from the space $W^{\al-1}_{2}(0,1)$, $\al\in[0,1]$,
and Dirichlet or Neumann--Dirichlet boundary conditions. We also give
application of the obtained results to the inverse spectral problem of
recovering the potential from these two spectra.
