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Constrained clustering has been an active research topic since the last decade. Most studies focus on batch-mode algorithms. This brief introduces two algorithms for on-line constrained learning, named on-line linear constrained vector quantization error (O-LCVQE) and constrained rival penalized competitive learning (C-RPCL). The former is a variant of the LCVQE algorithm for on-line settings, whereas the latter is an adaptation of the (on-line) RPCL algorithm to deal with constrained clustering. The accuracy results-in terms of the normalized mutual information (NMI)-from experiments with nine datasets show that the partitions induced by O-LCVQE are competitive with those found by the (batch-mode) LCVQE. Compared with this formidable baseline algorithm, it is surprising that C-RPCL can provide better partitions (in terms of the NMI) for most of the datasets. Also, experiments on a large dataset show that on-line algorithms for constrained clustering can significantly reduce the computational time.