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Transient gain response of optical amplifiers to the addition/removal of channels is a major problem in multi-wavelength amplified optical networks. In order to avoid error bursts in the surviving channels, signal power fluctuations due to channel addition or removal caused by network reconfigurations or line failures must be minimised. The authors analyse the recently proposed and experimentally tested gain-locking technique for Raman fibre amplifiers, based on surviving channel power monitoring and pump power control. The analysis is based on the application of a comprehensive large-signal numerical model, which incorporates temporal properties and downstream propagation of multiple signals, upstream propagation of multiple pumps and downstream and upstream propagation of amplified spontaneous emission (ASE) spectral components in a Raman fibre amplifier. It follows from the theoretical investigation that the peak-to-peak surviving channel power excursion can be reduced to less than 0.2 dB for the addition/removal of 50% of channels when the pump power feedback parameters are appropriately selected.