Abstract: Let $\Waff$ be an affine Weyl group, and let $C$ be a left, right, or two-sided Kazhdan--Lusztig cell in $\Waff$. Let $\Reduced (C)$ be set of all reduced expressions of elements of $C$, regarded as a formal language in the sense of the theory of computation. We show that $\Reduced (C)$ is a regular language. Hence the reduced expressions of the elements in any Kazhdan--Lusztig cell can be enumerated by a finite state automaton.