Two neural network approaches, Kohonen's Self-Organizing (Feature) Map (SOM) and the Topology Representing Network (TRN) of Martinetz and Schulten are employed in the context of competitive market structuring and segmentation analysis. In an empirical study using brands preferences derived from household panel data, we compare the SOM and TRN approach to MULTICLUS, a parametric approach which also simultaneously solves the market structuring and segmentation problem. Our empirical analysis shows several benefits and shortcomings of the three methodologies under investigation, MULTICLUS, SOM, and TRN. As compared to MULTICLUS, we find that the non-parametric neural network approaches show a higher robustness against any kind of data preprocessing and a higher stability of partitioning results. As compared to SOM, we find advantages of TRN which uses a more flexible concept of adjacency structure. In TRN, no rigid grid of units must be specified. A further advantage of TRN lies in the possibility to exploit the information of the neighborhood graph which supports ex-post decisions about the segment configuration at both the micro and the macro level. However, SOM and TRN also have some drawbacks as compared to MULTICLUS. The network approaches are, for instance, not accessible to inferential statistics. Our empirical study indicates that especially TRN may represent a useful expansion of the marketing analysts tool box.