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This paper presents an adaptive neural network (NN) approach for the behavioral modeling of wireless transmitters exhibiting dynamic nonlinearities that are mainly caused by the power amplifier (PA). The proposed distributed spatiotemporal NN mimics the functionality of the mammal cerebellum, which is capable of very fast learning and contains features of interpolation. PAs' memory effects are modeled by using linear affine projection on a local function generated by preceding signal inputs. The applicability of the proposed model is validated in the frequency and time domains for forward and reverse modeling using a highly nonlinear Doherty amplifier and a class AB PA driven by wideband code division multiple access and WiMAX signals. The modeling performance is compared with existing techniques to establish it as a successful model that requires a relatively less demanding processing speed and memory requirement during the identification procedure. This model was found to be effective for adaptive applications such as baseband predistortion-based linearization of wireless transmitters.