  We prove that the Nielsen zeta function is a rational function or a radical
of a rational function for orientation preserving homeomorphisms on closed
orientable 3-dimensional manifolds which are special Haken or Seifert
manifolds. In the case of pseudo-Anosov homeomorphism of surface we compute an
asymptotic for the number of twisted conjugacy classes or for the number of
Nielsen fixed point classes whose norm is at most $x$.
