Large-scale distributed training of deep acoustic models plays an important role in today's high-performance automatic speech recognition (ASR). In this paper we investigate a variety of asynchronous decentralized distributed training strategies based on data parallel stochastic gradient descent (SGD) to show their superior performance over the commonly-used synchronous distributed training via allreduce, especially when dealing with large batch sizes. Specifically, we study three variants of asynchronous decentralized parallel SGD (ADPSGD), namely, fixed and randomized communication patterns on a ring as well as a delay-by-one scheme. We introduce a mathematical model of ADPSGD, give its theoretical convergence rate, and compare the empirical convergence behavior and straggler resilience properties of the three variants. Experiments are carried out on an IBM supercomputer for training deep long short-term memory (LSTM) acoustic models on the 2000-hour Switchboard dataset. Recognition and speedup performance of the proposed strategies are evaluated under various training configurations. We show that ADPSGD with fixed and randomized communication patterns cope well with slow learners. When learners are equally fast, ADPSGD with the delay-by-one strategy has the fastest convergence with large batches. In particular, using the delay-by-one strategy, we can train the acoustic model in less than 2 hours using 128 V100 GPUs with competitive word error rates.