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If a frequency band has primary and secondary users, then the cognitive radios of the secondary users must monitor the band and be prepared to cease their transmissions if a primary user's radio begins to transmit. Traditional spectrum sensing requires the secondary radios to refrain from communicating while they check for the emergence of primary signals. We propose and evaluate methods by which the secondary radios can continue their communications while simultaneously monitoring the band to detect any transmissions that are initiated by the primary radios. Our methods for spectrum monitoring supplement traditional spectrum sensing and improve the communications efficiency of the secondary radios.