Time-Varying Neural Network (TV-NN) is a novel structure applied to nonstationary system identification tasks. Up to date, there are two main categories of approaches to train TV-NN: Gradient-based and ELM-based. Among the latter, the variants EM-ELM-TV and EM-OB have been recently proposed by the authors to determine the number of hidden nodes and the number of output bases functions automatically, which are important parameters to be preset in standard ELM. The aim of this contribution consists in evaluating the performances of aforementioned ELM-based algorithms in training TV-NNs to identify nonstationary Volterra systems, which are used to model a wide category of nonstationary nonlinear systems. Simulation results show that with polynomial activation function, ELM-based algorithms are able to attain good generalization performances in the addressed identification problem.