Subband adaptive algorithms have been developed for applications such as acoustic echo cancellation and wideband active noise control, which require adaptive filters with thousands of taps resulting in high computational complexity and slow adaptation convergence. By using subband adaptive algorithms, both computational complexity and convergence rate may be reduced. Structures with non-critical sampling of the subband signals have been frequently employed in order to avoid aliasing effects. Recently, new subband structures with critical sampling have been developed in which the aliasing between adjacents subbands is completely canceled. In this paper, theoretical analyses of the convergence behaviors of subband adaptive algorithms with critical sampling are presented, from which the convergence rates and minimum mean-square errors can be estimated.