In this paper, we propose a novel method of blind signal separation using a new performance criterion with nonlinear separating functions, and derive an adaptive algorithm. The criterion consists of nonlinear mappings of output signals and their cumulants for independence of the signals. We show that our method requires a weak condition for stable separation through the ODE analysis. Simulation results are given to verify the validity and advantage of the proposed algorithm. (C) 1999 Elsevier Science B.V. All rights reserved.