The critical slowing down of anisotropic magnets, binary mixtures, and systems undergoing structural transitions is interpreted in terms of suitable defined clusters, their growth, and their motions (cluster reactions, cluster diffusion, and cluster waves). Our previous studies of the Glauber model are extended considerably by numerical calculations, including the use of the cluster model of Reatto and Rastelli. The behavior of the relaxation function is very insensitive to the details of the models used. A scaling theory of nonlinear response is given, which is far more general than the cluster dynamics treatment. Two different cases occur:(i) at fixed relative nonlinearity the critical exponents agree with the corresponding exponents of linear response; (ii) if the initial state is held fixed, different exponents are found, however, which agree with predictions of Racz, and are consistent with Monte Carlo simulations of the nonlinear slowing down of the energy in kinetic Ising models.