Individuals with hearing loss allocate cognitive resources to comprehend noisy speech in everyday life scenarios. Such a scenario could be when they are exposed to ongoing speech and need to sustain their attention for a rather long period of time, which requires listening effort. Two well-established physiological methods that have been found to be sensitive to identify changes in listening effort are pupillometry and electroencephalography (EEG). However, these measurements have been used mainly for momentary, evoked or episodic effort. The aim of this study was to investigate how sustained effort manifests in pupillometry and EEG, using continuous speech with varying signal-to-noise ratio (SNR). Eight hearing-aid users participated in this exploratory study and performed a continuous speech-in-noise task. The speech material consisted of 30-second continuous streams that were presented from loudspeakers to the right and left side of the listener (±30° azimuth) in the presence of 4-talker background noise (+180° azimuth). The participants were instructed to attend either to the right or left speaker and ignore the other in a randomized order with two different SNR conditions: 0 dB and -5 dB (the difference between the target and the competing talker). The effects of SNR on listening effort were explored objectively using pupillometry and EEG. The results showed larger mean pupil dilation and decreased EEG alpha power in the parietal lobe during the more effortful condition. This study demonstrates that both measures are sensitive to changes in SNR during continuous speech.