For many years now, subband and frequency-domain adaptive filtering techniques have been proposed for the identification of high-order FIR systems. Classical LMS-based algorithms are less attractive as their computational load is higher and their convergence behaviour for coloured inputs is worse. Subband processing has many desirable properties. However, when used to implement adaptive filters, various effects (such as residual errors and slow convergence due to aliasing) occur and reduce performance. On the other hand, it is known that frequency-domain adaptive filters do not suffer from these problems despite being (nearly) equivalent to subband adaptive filters, be it with "poor" filter banks (modulated sine frequency responses). In this paper the operation of the frequency-domain techniques are unravelled and explained in the "subband jargon" and among other things it will be shown how aliasing is compensated for in the frequency-domain approach. This paper aims at generalising frequency-domain aliasing-compensation techniques to subband adaptive systems. Further, some design criteria for subband adaptive systems are formulated. Three realisation conditions and an alternative adaptation scheme will be proposed. Standard subband adaptive filters cannot fulfil all conditions, whereas for frequency-domain-based algorithms the design criteria are met. (C) 2001 Elsevier Science B.V. All rights reserved.