  The influence of the additional second neighbor hopping t' on the spin
response of the t-J model in the underdoped and optimally doped regimes is
studied within the fermion-spin theory. Although the additional second neighbor
hopping t' is systematically accompanied with the reduction of the dynamical
spin structure factor and susceptibility, the qualitative behavior of the
dynamical spin structure factor and susceptibility of the t-t'-J model is the
same as in the case of t-J model. The integrated dynamical spin structure
factor spectrum is almost t' independent, and the integrated dynamical spin
susceptibility still shows the particularly universal behavior as
$I(\omega,T)\propto {\rm arctan}[a_{1}\omega/T+a_{3}(\omega/T)^{3}]$.
