Mistuning can produce a considerable increase of the vibratory forced response of the blades compared with that of the tuned bladed disk. This situation can lead to high cycle fatigue failure, and, therefore, it is of crucial importance for the prediction of the safe operation limit of the bladed disk. Nonlinear friction forces determine the final vibration amplitude of the blades, and, because of mistuning, the complete bladed disk has to be considered, increasing considerably the difficulty of the problem. For this reason, we consider the application of asymptotic multiple scale techniques to derive simplified models that give the final vibration states at a very low CPU cost. This asymptotic method is based on the idea that all significant effects (forcing, nonlinear friction damping, and mistuning) produce, in most practical situations, just small corrections of the tuned blade elastic oscillation. These small effects develop in a much longer time scale than that associated with the natural elastic frequency of the tuned system. The reduced models produced by this asymptotic methodology retain only the slow time dynamics, filtering out the fast scale oscillation. In this paper, the bladed disk is described using a mass-spring system with nonlinear friction and with an external forcing acting on a blade-dominated modal family where all modes have very similar vibration frequencies. The derivation of the asymptotic model from the mass-spring system is explained in detail, and validated against the results from the original mass-spring model.