A new neural-network approach is presented for extracting independent source signals one-by-one from a linear mixture of them when the number of noisy mixed signals is equal to or larger than the number of sources. In this approach, two types of cascade neural networks, having similar structures, are employed. The first cascade network performs prewhitening (preprocessing) of the mixed signals by sequentially extracting principal components. From the normalized (to unit variance) prewhitened signals, the second network, then sequentially extracts the original source signals in order according to their stochastic properties, namely, in decreasing order of absolute valves of normalized kurtosis. Extensive computer simulations confirm the validity and high performance of our approach.