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A class of variable step-size algorithms for complex-valued nonlinear neural adaptive finite impulse response (FIR) filters realised as a dynamical perceptron is proposed. The adaptive step-size is updated using gradient descent to give variable step-size complex-valued nonlinear gradient descent (VSCNGD) algorithms. These algorithms are shown to be capable of tracking signals with rich and unknown dynamics, and exhibit faster convergence and smaller steady state error than the standard algorithms. Further, the analysis of stability and computational complexity is provided. Simulations in the prediction setting support the approach.