Brain-computer interfaces (BCIs) for communication can be nonintuitive, often requiring the performance of hand motor imagery or some other conversation-irrelevant task. In this paper, electroencephalography (EEG) was used to develop two intuitive online BCIs based solely on covert speech. The goal of the first BCI was to differentiate between 10s of mental repetitions of the word "no" and an equivalent duration of unconstrained rest. The second BCI was designed to discern between 10s each of covert repetition of the words "yes" and "no". Twelve participants used these two BCIs to answer yes or no questions. Each participant completed four sessions, comprising two offline training sessions and two online sessions, one for testing each of the BCIs. With a support vector machine and a combination of spectral and time-frequency features, an average accuracy of 75.9% ± 11.4 was reached across participants in the online classification of no versus rest, with 10 out of 12 participants surpassing the chance level (60.0% for p < 0.05). The online classification of yes versus no yielded an average accuracy of 69.3% ± 14.1, with eight participants exceeding the chance level. Task-specific changes in EEG beta and gamma power in language-related brain areas tended to provide discriminatory information. To our knowledge, this is the first report of online EEG classification of covert speech. Our findings support further study of covert speech as a BCI activation task, potentially leading to the development of more intuitive BCIs for communication.