The paper provides comparison of three different approaches to on-line tuning of generalized adaptive notch filters (GANFs) - the algorithms used for identification/tracking of quasi-periodically varying dynamic systems. Tuning is needed to adjust adaptation gains, which control tracking performance of GANF algorithms, to the unknown and/or time time-varying rate of system nonstationarity. Two out of three compared approaches are classical solutions - the first one incorporates sequential optimization of adaptation gains while the second one is based on the concept of parallel estimation. The main contribution of the paper is that it suggests the third way - it shows that the best results can be achieved when both approaches mentioned above are combined in a judicious way. Such joint sequential/parallel optimization preserves advantages of both treatments: adaptiveness (sequential approach) and robustness to abrupt changes (parallel approach). Additionally the paper shows how, using the concept of surrogate outputs, one can extend the proposed single-frequency algorithm to the multiple frequencies case, without falling into the complexity trap known as the "curse of dimensionality". (C) 2008 Elsevier Ltd. All rights reserved.