  The repetition threshold of a class $C$ of infinite $d$-ary sequences is the
smallest real number $r$ such that in the class $C$ there exists a sequence
that avoids $e$-powers for all $e> r$. This notion was introduced by Dejean in
1972 for the class of all sequences over a $d$-letter alphabet. Thanks to the
effort of many authors over more than 30 years, the precise value of the
repetition threshold in this class is known for every $d \in \mathbb N$. The
repetition threshold for the class of Sturmian sequences was determined by
Carpi and de Luca in 2000. Sturmian sequences may be equivalently defined in
various ways, therefore there exist many generalizations to larger alphabets.
Rampersad, Shallit and Vandome in 2020 initiated a study of the repetition
threshold for the class of balanced sequences -- one of the possible
generalizations of Sturmian sequences. Here, we focus on the class of $d$-ary
episturmian sequences -- another generalization of Sturmian sequences
introduced by Droubay, Justin and Pirillo in 2001. We show that the repetition
threshold of this class is reached by the $d$-bonacci sequence and its value
equals $2+\frac{1}{t-1}$, where $t>1$ is the unique positive root of the
polynomial $x^d-x^{d-1}- \cdots -x-1$.
