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In this paper, a new class of models, named twin nonlinear two-box (TNTB) models, is proposed for modeling and digital predistortion of power amplifiers and transmitters exhibiting memory effects. The forward, reverse, and parallel TNTB models are introduced. These models enable a more general modeling of nonlinear distortions and memory effects in comparison with previously reported behavioural models. The models' performance is assessed experimentally for a high power Doherty amplifier driven by multi-carrier WCDMA signals. The modeling and predistortion results demonstrate the effectiveness of the proposed models when compared to the well established memory polynomials. Indeed, the proposed models lead to the same performance as memory polynomial models while reducing the number of parameters by approximately 50%. Definitely, only 24 parameters were required to accurately model and linearize a highly nonlinear Doherty power amplifier driven by a 20 MHz wide multi-carrier signal. To the best of the authors' knowledge, this is the lowest complexity model/digital predistorter reported for similar context.