Research on the impact of cognitive disorders associated with neurodegenerative disease, such as Alzheimer’s disease, on rhythmic abilities, yielded mixed results. This study aimed to test the impact of neurocognitive disorders on two rhythmic skills previously untested in elderly populations. First, a task involving synchronisation to music was employed, to identify a specific deficit in beat induction, which involves actively deducting an underlying rhythm in music (Toiviainen et al., 2020), distinct from automatic beat maintenance. Second, we used a beat misalignment detection test to evaluate rhythm perception without production. To this end, 87 patients (mean age = 81) with cognitive disorders of varying severity (MMSE from 16 to 30) from a geriatric day hospital underwent a sensorimotor synchronisation task with three levels of beat saliency (BS; metronome; music with high BS; and music with low BS) and an evaluation of beat perception. Mixed-effects models revealed an interaction between beat saliency and MMSE on synchronisation consistency. As expected, the highest consistency was observed when tapping to a metronome, followed by high BS music, and the lowest with low BS music (p < .001). Additionally, consistency decreased with lower MMSE scores, but only with low BS music (p < .001).With regard to beat perception, as assessed by the Beat Alignment Test, MMSE was negatively related to the number of false alarms (incorrect reports of alignment; p < .05). Our findings suggest that during synchronisation to music, beat maintenance remains preserved in individuals with impaired cognitive functioning. In contrast, those individuals may experience difficulty with beat induction and the perception of beat alignment. These results will be discussed in light of current theories of rhythm and their potential clinical implications.