Two types of pointwise a posteriori error estimates are presented for gradients of finite element approximations of second-order quasilinear elliptic problems. We first give a global residual estimator which is equivalent to the global maximum norm of the gradient error up to higher-order terms. The second type of residual estimator is designed to control the pointwise gradient error locally over subdomains. It is a novel a posteriori counterpart to the localized or weighted a priori estimates recently proven by Schatz. This estimator is shown to be equivalent up to higher-order terms to the error measured in a weighted global norm which depends on the subdomain of interest.