We characterize in this paper the credibility of incentive equilibrium strategies for the class of linear-state differential games. We derive a general condition for credibility and illustrate its use on two differential games taken from the literature of respectively environmental economics and knowledge accumulation. We show that the proposed linear incentive strategies are not always credible. Further, we provide alternative nonlinear credible strategies which suggest that we should not stick only to linear incentive strategies even in a simple class of differential games such as the linear-state one.