  In this paper, we consider gradient estimates for two type of nonlinear
parabolic equations under the Ricci flow: one is the equation $$u_t=\Delta
u+au\log u+bu$$ with $a,b$ two real constants, the other is $$u_t=\Delta
u+\lambda u^{\alpha}$$ with $\lambda,\alpha$ two real constants. By a suitable
scaling for the above two equations, we obtain Hamilton-Souplet-Zhang type
gradient estimates.
