Time Delay Neural Networks (TDNNs) are widely used in both DNN-HMM based hybrid speech recognition systems and recent end-to-end systems. Nevertheless, the receptive fields of TDNNs are limited and fixed, which is not desirable for tasks like speech recognition, where the temporal dynamics of speech are varied and affected by many factors. This paper proposes to use deformable TDNNs for adaptive temporal dynamics modeling in end-to-end speech recognition. Inspired by deformable ConvNets, deformable TDNNs augment the temporal sampling locations with additional offsets and learn the offsets automatically based on the ASR criterion, without additional supervision. Experiments show that deformable TDNNs obtain state-of-the-art results on WSJ benchmarks (1.42%/3.45% WER on WSJ eval92/dev93 respectively), outperforming standard TDNNs significantly. Furthermore, we propose the latency control mechanism for deformable TDNNs, which enables deformable TDNNs to do streaming ASR without accuracy degradation.