This paper develops a framework for the mean-square analysis of adaptive filters with general data and error nonlinearities. The approach relies on energy conservation arguments and is carried out without restrictions on the probability distribution of the input sequence. In particular, for adaptive filters with diagonal matrix nonlinearities, we provide closed form expressions for the steady-state performance and necessary and sufficient conditions for stability. We carry out a similar study for long adaptive filters that employ error nonlinearities relying on a weaker form of the independence assumption. We provide expressions for the steady-state error and bounds on the step-size for stability by exploiting the Cramer-Rao bound of the underlying estimation process.