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Covert communications are conducted at a low received signal-to-noise ratio (SNR) to prevent interception or detection by an eavesdropper, and successful detection in this particular area heavily relies on the processing gain achieved by employing the direct-sequence spread-spectrum (DSSS) technique. If covert communications take place in underwater acoustic (UWA) environments, then additional challenges are present. UWA channels are time-varying in nature, which could preclude an accurate channel estimation at low SNR. Furthermore, UWA environments are frequency-selective with long-memory channels, which imposes challenges to the design of the spreading waveform. In this paper, we investigate covert UWA communications from a noncoherent perspective. Two modulation schemes are addressed, namely, binary orthogonal modulation and binary differential phase-shift keying (DPSK). Both schemes are coupled with the DSSS technique and a RAKE receiver. The employed spreading waveforms not only account for the transceiver structure and frequency-selective nature of the UWA channel, but also serve to protect the privacy of the transmitted information. The effectiveness of the proposed methods is verified by numerical examples.