Clustering algorithms of the Neural Gas (NG) type take into consideration the dissimilarities between prototypes in the original input space. It has been successfully applied in vector quantisation, topology creation as well as clustering. NG algorithms conventionally are based on the squared Euclidean distance or L2, which have several known setbacks (not robust to noise and outliers). Our goal is to introduce new NG clustering algorithms (on-line and batch) based on the L1 distance (robust to noise and outliers). We propose three Neural Gas algorithms based on the L1 distance using two different algorithms to find the optimal prototypes and compare them with another well-known clustering algorithm. Given the experiments performed, the proposed methods showed a competitive performance. Preliminary results indicate that research on Neural Gas algorithms based on L1 distance is promising.