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Cross-band modulation effects in the concurrent dual-band transmitters are quite noticeable for the linearization. This paper proposes a novel two-dimensional modified memory polynomial (2D-MMP) technique to compensate for nonlinear distortion in the concurrent dual-band transmitters. By taking into account the cross-band modulation effects, the 2D-MMP model is developed by properly modifying the envelope terms of the conventional memory polynomial (MP) model. This makes the model complexity of the 2D-MMP model significantly reduced compared to the prior 2D-DPD model in previous work. However, the linearization ability of the 2D-MMP model is still retained. Simulations prove that the 2D-MMP model is quite robust to different PA models. Experimental measurements were carried out for a dual-band class-AB PA exhibiting mild nonlinearity and a highly nonlinear dual-band Doherty PA. The results show that the 2D-MMP model can achieve nearly the same linearization accuracy compared to the 2D-DPD model, with much less coefficients. Less than -52 dBc adjacent channel power ratios (ACPRs) for the dual-band class-AB power amplifiers (PAs) and -50 dBc ACPRs for the dual-band Doherty PA in the dual bands were achieved.