In the high bit-rate data compression, the filterbanks that match the statistical properties of inputs have been widely researched. For orthonormal uniform filterbanks and biorthogonal filterbanks without order constraints, the design problems have been solved on the whole. However, for biorthogonal FIR filterbanks, an efficient method associated with an algorithm for the design still needs to be developed. In this paper, two-channel adaptive biorthogonal filterbanks via lifting scheme are investigated. Starting from an arbitrary filterbank (orthonormal or biorthogonal), two-channel biorthogonal filterbanks are designed by the adaptive lifting scheme, which is a general form of our previous work. Two adaptive lifting algorithms are developed, namely, the sequential adaptive lifting and the joint adaptive lifting. Further, it is proved that starting from a linear-phase filterbank, the optimal filterbank by the sequential adaptive lifting preserves the linear-phase property. Experimental results show that the subband coding gains can be markedly improved when an appropriate initial filterbank is chosen. © 2002 Elsevier Science B.V. All rights reserved.