Abstract: Online Infomax and extended Infomax algorithms are applied widely to signal separation at nonstationary circumstance. A new block-adaptive online ICA algorithm is proposed which combines the benefits of batch processing and adaptive online processing. In this paper, we deduce the blockadaptive online updating formulae of Infomax and extend Infomax algorithms in detail and introduce a step-size updating regulation which is based on the kurtosis covariance of ouputs. The computer simulations show that the new algorithms can apply to nonstationary circumstance like other online algorithms and the speed of separating signals of the new algorithm is much faster than the old one with the same performance.