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Alzheimer's disease (AD) is a neurodegenerative disorder characterized by a progressive cognitive decline, mostly prominent in the domain of memory, but also associated with other cognitive deficits and non-cognitive symptoms. Reduced muscle strength is common in AD. However, the current understanding of its relationship with cognitive decline is limited. This study investigates the relationship between muscle strength and cognition in patients with AD and mild cognitive impairment (MCI). We enrolled 148 consecutive subjects, including 74 patients with probable AD dementia, 37 MCI, and 37 controls. Participants underwent neuropsychological evaluation focused on attention, working memory, declarative memory and learning. Muscle strength and muscle mass were measured through hand dynamometer and bio-electrical impedance analysis, respectively. Patients with AD dementia were divided with respect to the severity of cognitive impairment into mild and moderate-to-severe patients. Moderate-to-severe patients with AD presented lower handgrip strength than MCI and controls. No differences were observed in muscle mass. In MCI and AD dementia, handgrip strength was associated with overall cognitive functioning, attentional and memory performance. The routine implementation of handgrip strength assessment in the clinical work-up of patients with MCI and AD could potentially represent a simple method to monitor functional and cognitive decline along the disease course.