This work addresses the challenge of modelling Hammerstein nonlinear systems iteratively, combining a kernel adaptive filter with a linear filter. We evaluate this approach in the context of acoustic echo cancellation (AEC), where a nonlinear speaker followed by a linear system models the loudspeaker enclosure microphone system (LEMS). Our contributions include a novel iterative online processing procedure and a detailed investigation of challenges and strategies, such as offset removal and normalization, for improving system stability and performance. Our results demonstrate that normalization is crucial for reducing fluctuations and achieving a 5 dB improvement in Echo Return Loss Enhancement (ERLE) compared to linear filters.