In this paper, we address the problem of automatically detecting whether the audio and visual speech modalities in frontal pose videos are synchronous or not. This is of interest in a wide range of applications, for example spoof detection in biometrics, lip-syncing, speaker detection and diarization in multi-subject videos, and video data quality assurance. In our adopted approach, we investigate the use of deep neural networks (DNNs) for this purpose. The proposed synchrony DNNs operate directly on audio and visual features over relatively wide contexts, or, alternatively, on appropriate hidden (bottleneck) or output layers of DNNs trained for single-modal or audio-visual automatic speech recognition. In all cases, the synchrony DNN classes consist of the "in-sync" and a number of "out-of-sync" targets, the latter considered at multiples of ± 30 msec steps of overall asynchrony between the two modalities. We apply the proposed approach on two multi-subject audio-visual databases, one of high-quality data recorded in studio-like conditions, and one of data recorded by smart cell-phone devices. On both sets, and under a speaker-independent experimental framework, we are able to achieve very low equal-error-rates in distinguishing "in-sync" from "out-of-sync" data.