This paper addresses the issue of equalization of highspeed data-communications systems (e.g. Digital Subscriber Line) under dynamic channel conditions, where the modulation format is Quadrature Amplitude Modulation (QAM). In particular, the focus is on systems that use a combination of Forward Error Correction and Tomlinson-Harashima Precoding to achieve the necessary performance. Previous work by the authors using Pulse Amplitude Modulation (PAM) has shown that such systems operating with a fixed precoder will suffer significant performance degradation in certain cases where the channel changes during run-time. Furthermore, the effects of these channel changes may be minimised using a novel adaptive precoder architecture. This paper extends the previous work to the case of 2-dimensional QAM, and shows that the proposed adaptive precoder algorithm allows the QAM system to rapidly respond to dynamic channel conditions, thus minimising the impact of channel changes on overall system performance.