Abstract: Based on the analysis of Chebyshev orthogonal polynomial neural network nonlinear filter,and by using the fast approximation characteristics of Legendre orthogonal polynomial and the structrue of decision feedback equalizer,two nonlinear equalizers with new structures are proposed,and an adaptive algorithm is deduced with the normalized least mean squares(NLMS).Simulations show that the equalization performances of the adaptive equalizers based on Legendre neural network and Chebyshev neural network are very approximate no matter the channel is linear or nonlinear,and the adaptive decision feedback equalizer based on Legendre orthogonal polynomial neural network can more effectively remove the nonlinear disturbance and intersymbol interference(ISI) and impove the performance of bit error ratio(BER).