We consider an industrial context where we deal with a stream of unlabelled documents that become available progressively over time. Based on an adaptive incremental neural gas algorithm (AING), we propose a new stream-based semisupervised active learning method (A2ING) for document classification, which is able to actively query (from a human annotator) the class-labels of documents that are most informative for learning, according to an uncertainty measure. The method maintains a model as a dynamically evolving graph topology of labelled document-representatives that we call neurons. Experiments on different real datasets show that the proposed method requires on average only 36.3% of the incoming documents to be labelled, in order to learn a model which achieves an average gain of 2.15-3.22% in precision, compared to the traditional supervised learning with fully labelled training documents.