Hammerstein nonlinear systems have been widely used in different nonlinear system model. Hence, this work investigates an iterative modelling approach for such systems, combining a kernel adaptive filter with a linear filter. Unlike previous cascaded approaches that employ kernel and linear filters, which typically rely on batch processing, this paper proposes a sample-by-sample adaptation of the kernel and linear filter. This approach was evaluated in the context of acoustic echo cancellation (AEC), where a speaker exhibiting saturation nonlinearities, in cascade with a linear system, models the loudspeaker enclosure microphone system (LEMS). The contributions include a novel iterative online kernel coefficients updating procedure and a detailed investigation of challenges and strategies like offset removal and normalization, all aimed at improving system stability and performance. Our results demonstrate that normalization significantly reduces fluctuations, leading to over 10 dB improvement in convergence (measured by system distance) during the intermediate phase. It also provides a 5 dB Echo Return Loss Enhancement (ERLE) gain over linear filters when clipping occurs.