The paper proposes a "neural transducer" model for sequence-to-sequence tasks that operates in a left-to-right and on-line fashion. In other words, the model produces output as the input is received instead of waiting until the full input is received like most sequence-to-sequence models do. Key ideas used to make the model work include a recurrent attention mechanism, the use of an end-of-block symbol in the output alphabet to indicate when the transducer should move to the next input block, and approximate algorithms based on dynamic programming and beam search for training and inference with the transducer model. Experiments on the TIMIT speech task show that the model works well and explore some of the design parameters of the model. Like similar models of this type, the input is processed by an encoder and a decoder produces an output sequence using the information provided by the encoder and conditioned on its own previous predictions. The method is evaluated on a toy problem and the TIMIT phoneme recognition task. The authors also propose some smaller ideas like two different attention mechanism variations. The map from block input to output is governed by a standard sequence-to-sequence model with additional state carried over from the previous block. Alignment of the two sequences is approximated by a dynamic program using a greedy local search heuristic. Experimental results are presented for phone recognition on TIMIT. The encoder is a multi-layer LSTM RNN. The decoder is an RNN model conditioned on weighted sums of the last layer of the encoder and it's previous output. The weighting schemes (attention) varies and can be conditioned on the hidden states or also previous attention vectors. The decoder model produces a sequence of symbols, until it outputs a special end character "e" and is moved to the next block (other mechanisms where explored as well (no end-of-block-symbol and separately predicting the end of a block given the attention vector). It is then fed the weighted sum of the next block of encoder states. The resulting sequence of symbols determines an alignment of the target symbols over the blocks of inputs, where each block may be assigned a variable number of characters. The system is trained by fixing an alignment, that approximately resembles the best alignment. Finding this approximately best alignment is akin to a beam-search with a beam size of M (line 169), but a restricted set of symbols conditional on the last symbol in a particular hypothesis (since the target sequence is known). Alignments are computed less frequently than model updates (typically every 100 to 300 sequences). For inference, an unconstrained beam-search procedure is performed with a threshold on sequence length and beam size.