We recently showed that Long Short-Term Memory (LSTM) recurrent neural networks (RNNs) outperform state-of-the-art deep neural networks (DNNs) for large scale acoustic modeling where the models were trained with the cross-entropy (CE) criterion. It has also been shown that sequence discriminative training of DNNs initially trained with the CE criterion gives significant improvements. In this paper, we investigate sequence discriminative training of LSTM RNNs in a large scale acoustic modeling task. We train the models in a distributed manner using asynchronous stochastic gradient descent optimization technique. We compare two sequence discriminative criteria -- maximum mutual information and state-level minimum Bayes risk, and we investigate a number of variations of the basic training strategy to better understand issues raised by both the sequential model, and the objective function. We obtain significant gains over the CE trained LSTM RNN model using sequence discriminative training techniques.