Natural language inference aims to predict whether a premise sentence can infer another hypothesis sentence. Existing methods typically have framed the reasoning problem as a semantic matching task. The both sentences are encoded and interacted symmetrically and in parallel. However, in the process of reasoning, the role of the two sentences is obviously different, and the sentence pairs for NLI are asymmetrical corpora. In this paper, we propose an asynchronous deep interaction network (ADIN) to complete the task. ADIN is a neural network structure stacked with multiple inference sub-layers, and each sub-layer consists of two local inference modules in an asymmetrical manner. Different from previous methods, this model deconstructs the reasoning process and implements the asynchronous and multi-step reasoning. Experiment results show that ADIN achieves competitive performance and outperforms strong baselines on three popular benchmarks: SNLI, MultiNLI, and SciTail.