An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form t+（t²） is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ，σ ）  , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .