  In this paper, we discuss the relationship between Li-Yorke chaos and
distributional chaos in a sequence. We point out the set of all distributional
$\delta$-scramble pairs in the sequence $Q$ is a $G_\delta$ set, and prove that
Li-Yorke $\delta$-chaos is equivalent to distributional $\delta$-chaos in a
sequence, a uniformly chaotic set is a distributional scramble set in some
sequence and a class of transitive system implies distributional chaos in a
sequence.
