A novel generalized two dimensional (2-D) digital predistortion (DPD) architecture for concurrent dual-band transmitters is presented. The proposed architecture is based on simultaneous injection of in-band intermodulation (IM) and cross-modulation (CM) distortion products. A general fundamental-frequency model for concurrent dual-band transmitter is developed theoretically and proofed experimentally. An individual impact of each IM and CM distortion component is theoretically derived and analyzed. It is clearly proven by theoretical analysis and experiments that the proposed predistorter improves the in-band and out-of-band performances of both signals. The simulation and experimental studies are performed using various signal sets. The proposed predistorter does not depend on frequency separation between bands and has low computational complexity in comparison with concurrent dual-band DPD's state-of-the-art. In addition, it is clearly shown in experiments that when using iterative simultaneous injections, a phenomenon known as distortion compensation limit can be reduced. A presence of memory effects and their mitigation in frequency domain for each band of concurrent dual-band transmitter are also demonstrated in experiments.