  In this note we obtain gradient estimates for the heat semigroup on
nonisotropic Heisenberg groups. More precisely, our aim is to get the H.-Q. Li
inequality on nonisotropic Heisenberg groups, which is a generalization of the
original result on the classical Heisenberg group of dimension 3 and a
counterpart of the inequality on the H-type groups. Our proof is based on a
Cheeger type inequality, which is an approach proposed by Bakry et al.
