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We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.