Machine learning has achieved significant success in electroencephalogram (EEG) based brain-computer interfaces (BCIs), with most existing research focusing on improving the decoding accuracy. However, recent studies have shown that EEG-based BCIs are vulnerable to adversarial attacks, where small perturbations added to the input can cause misclassification. Detecting adversarial examples is crucial for both understanding this phenomenon and developing effective defense strategies. This paper, for the first time, explores adversarial detection in EEG-based BCIs. We extend several popular adversarial detection approaches from computer vision to BCIs. Two new Mahalanobis distance based adversarial detection approaches, and three cosine distance based adversarial detection approaches, are also proposed, which showed promising performance in detecting three kinds of white-box attacks. We evaluated the performance of eight adversarial detection approaches on three EEG datasets, three neural networks, and four types of adversarial attacks. Our approach achieved an area under the curve (AUC) score of up to 99.99% in detecting white-box attacks. Additionally, we assessed the transferability of different adversarial detectors to unknown attacks. Through extensive experiments, we found that white-box attacks may be easily detected, and differences exist in the distributions of different types of adversarial examples. Our work should facilitate understanding the vulnerability of existing BCI models and developing more secure BCIs in the future.