Blind source separation (BSS) tries to transform a mixed random vector in order to recover the original independent sources. We present a new approach to linear BSS by using either a self-organizing map (SOM) or a neural gas (NG). In comparison to other mixture-space analysis (’geometric’) algorithms, these result in a considerable improvement in separation quality, although the computational cost is rather high. One goal of these algorithms is to establish connections between neural networks and BSS that could further be exploited by for example transferring convergence proofs for SOMs to geometric BSS algorithms.