  In this paper, it is shown that if a dynamical system is null and distal,
then it is equicontinuous. It turns out that a null system with closed proximal
relation is mean equicontinuous. As a direct application, it follows that a
null dynamical system with dense minimal points is also mean equicontinuous.
Meanwhile, a distal system with trivial $\text{Ind}_{fip}$-pairs, and a
non-trivial regionally proximal relation of order $\infty$ is constructed.
