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Popular solutions to Named Entity Recognition (NER) include conditional random fields, sequence-to-sequence models, or utilizing the question-answering framework. However, they are not suitable for nested and overlapping spans with large ontologies and for predicting the position of the entities. To fill this gap, we introduce a new model for NER task -- an RNN transducer (RNN-T). These models are trained using paired input and output sequences without explicitly specifying the alignment between them, similar to other seq-to-seq models. RNN-T models learn the alignment using a loss function that sums over all alignments. In NER tasks, however, the alignment between words and target labels are available from the human annotations. We propose a fixed alignment RNN-T model that utilizes the given alignment, while preserving the benefits of RNN-Ts such as modeling output dependencies. As a more general case, we also propose a constrained alignment model where users can specify a relaxation of the given input alignment and the model will learn an alignment within the given constraints. In other words, we propose a family of seq-to-seq models which can leverage alignments between input and target sequences when available. Through empirical experiments on a challenging real-world medical NER task with multiple nested ontologies, we demonstrate that our fixed alignment model outperforms the standard RNN-T model, improving F1-score from 0.70 to 0.74.