Let $mathbb{A}=mathbb{F}_q$[T] be the polynomial ring over a finite field $mathbb{F}_q$[T] and K=$mathbb{F}_q$(T) its field of fractions. Let ${ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{in}{mathbb{A}}$ with deg $P{equiv}0$ (mod ${ell})$. In this paper we define the group $C_K$ of circular units in K=k$({sqrt[{ell}]P;:;P{in}J})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.