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Highlights• Solution for the jitter problem of the stimulus onsets for ERP single-trial detection.• Shift-invariant features based on the power spectrum or bispectrum.• AUC stability across stimulus onsets shifts 200ms.Non-invasive brain-computer interface (BCI) is a relatively new type of human-computer interaction. BCIs that are based on the detection of event-related potentials (ERPs) are usually synchronous. They require the knowledge of the stimulus onsets that evoke ERPs, which is time locked to the presence of a potentially relevant stimulus. The detection of ERPs like the P300 has been successfully used in BCI thanks to the oddball paradigm. The time locked detection is directly related to the synchronous aspect of a BCI. However, asynchronous detection is a critical issue in developing BCIs for real-life applications, where the machine should be able to detect the presence of an ERP independently from the knowledge of the stimulus onsets, or when wireless devices do not allow a precise knowledge of the stimulus onsets. Although the detection of single-trial ERP is already a challenge, when the stimulus onsets are well identified, we propose to investigate further the detection of single-trial ERP by considering different time locked stimuli. We propose and compare shift invariant ERP detection strategies on data from ten subjects obtained in a P300 speller experiment. With a shift invariant distance, we show that it is possible to obtain an AUC of 0.834 while allowing a jitter of ±40 ms. With inputs in the Fourier domain, the mean area under the ROC curves of 0.683 allowing a jitter of ±200 ms in the stimulus onsets. The results support the conclusion that ERP detection can be achieved without a precise knowledge of the stimulus onsets, and hence can be used with EEG amplifiers that do not allow a precise synchronization between the EEG signal and stimulus onsets.