  The effect of the additional second neighbor hopping t' on the spin dynamics
in the t-J model 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 behaviors of the dynamical spin structure factor and susceptibility
are the same as in the case of t-J model. It is also shown that the integrated
dynamical spin structure factor is almost t' independent in the underdoped
regime.
