In this correspondence, we propose a new allpass-based structure for the IIR Mth- and 2Mth-band filters. These filters consist of M allpass filters and an interpolation filter(sum of two allpasses). Consequently, the proposed structure is very efficient in implementation. By choosing the allpass phase appropriately, the resulting phase response of the IIR Mth-band filter becomes approximately linear. An example is designed and compared with FIR Mth-band filters.