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In this paper, channel estimation for two-way relay networks (TWRNs) over time-varying channels is investigated. We consider the amplify-and-forward (AF) relaying scheme and adopt the complex-exponential basis expansion model (CE-BEM) that represents the time-varying channel by a finite number of parameters. We develop the estimation methods for both the cascaded channels and the individual channels and also apply the total least square (TLS) algorithm to improve the estimation accuracy. Moreover, the training design is discussed and a heuristic criterion is proposed to minimize the condition number of the estimation matrix. The simulation results verify the goodness of the criterion.