In this paper, we discuss a general approach to the macroscopic traffic flow stability analysis of adaptive cruise controlled (ACC) vehicles. We present a macroscopic model with velocity saturation for traffic flow in which each individual vehicle is controlled by an ACC spacing policy. A nonlinear traffic flow stability criterion is investigated using a wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for a generalized ACC traffic flow model. The newly derived stability results are in agreement with previously derived results that were obtained using both microscopic and macroscopic models with a constant time headway (CTH) policy. Moreover, the stability results derived in this paper provide sufficient and necessary conditions for ACC traffic flow stability, which can be used to design other ACC spacing policies.