This paper is intended to present a new harmonic selection technique when solving nonlinear dynamic systems with the harmonic balance method. This technique belongs to the class of method called the adaptive harmonic balance method (AHBM). The harmonic selection is based on the use of a tangent predictor and relies on a stepwise regression procedure that allows for a dynamic management of the number of selected harmonics via an addition or removal procedure. The efficiency of this method relative to the classical harmonic balance method (HBM) is then evaluated through examples; this later step will indicate that AHBM can significantly reduce the number of variables, thus leading to computational time savings without deteriorating solution quality.