Converging evidence from structural, metabolic and functional connectivity MRI suggests that neurodegenerative diseases, such as Alzheimer's disease, target specific neural networks. However, age-related network changes commonly co-occur with neuropathological cascades, limiting efforts to disentangle disease-specific alterations in network function from those associated with normal ageing. Here we elucidate the differential effects of ageing and Alzheimer's disease pathology through simultaneous analyses of two functional connectivity MRI datasets: (i) young participants harbouring highly-penetrant mutations leading to autosomal-dominant Alzheimer's disease from the Dominantly Inherited Alzheimer's Network (DIAN), an Alzheimer's disease cohort in which age-related comorbidities are minimal and likelihood of progression along an Alzheimer's disease trajectory is extremely high; and (ii) young and elderly participants from the Harvard Aging Brain Study, a cohort in which imaging biomarkers of amyloid burden and neurodegeneration can be used to disambiguate ageing alone from preclinical Alzheimer's disease. Consonant with prior reports, we observed the preferential degradation of cognitive (especially the default and dorsal attention networks) over motor and sensory networks in early autosomal-dominant Alzheimer's disease, and found that this distinctive degradation pattern was magnified in more advanced stages of disease. Importantly, a nascent form of the pattern observed across the autosomal-dominant Alzheimer's disease spectrum was also detectable in clinically normal elderly with clear biomarker evidence of Alzheimer's disease pathology (preclinical Alzheimer's disease). At the more granular level of individual connections between node pairs, we observed that connections within cognitive networks were preferentially targeted in Alzheimer's disease (with between network connections relatively spared), and that connections between positively coupled nodes (correlations) were preferentially degraded as compared to connections between negatively coupled nodes (anti-correlations). In contrast, ageing in the absence of Alzheimer's disease biomarkers was characterized by a far less network-specific degradation across cognitive and sensory networks, of between- and within-network connections, and of connections between positively and negatively coupled nodes. We go on to demonstrate that formalizing the differential patterns of network degradation in ageing and Alzheimer's disease may have the practical benefit of yielding connectivity measurements that highlight early Alzheimer's disease-related connectivity changes over those due to age-related processes. Together, the contrasting patterns of connectivity in Alzheimer's disease and ageing add to prior work arguing against Alzheimer's disease as a form of accelerated ageing, and suggest multi-network composite functional connectivity MRI metrics may be useful in the detection of early Alzheimer's disease-specific alterations co-occurring with age-related connectivity changes. More broadly, our findings are consistent with a specific pattern of network degradation associated with the spreading of Alzheimer's disease pathology within targeted neural networks.