Down's syndrome is associated with pathological ageing and a propensity for early‐onset Alzheimer's disease. The early symptoms of dementia in people with Down's syndrome may reflect frontal lobe vulnerability to amyloid deposition. Auditory predictive processes rely on the bilateral auditory cortices with the recruitment of frontal cortices and appear to be impaired in pathologies characterized by compromised frontal lobe. Hence, auditory predictive processes were investigated to assess Down's syndrome pathology and its relationship with pathological ageing. An auditory electroencephalography (EEG) global–local paradigm was presented to the participants, in which oddball stimuli could either violate local or higher level global rules. We characterised predictive processes in individuals with Down's syndrome and their relationship with pathological ageing, with a focus on the EEG event‐related potential called Mismatch Negativity (MMN) and the P300. In Down's syndrome, we also evaluated the EEG components as predictor of cognitive decline 1 year later. We found that predictive processes of detection of auditory violations are overall preserved in Down's syndrome but also that the amplitude of the MMN to local deviancies decreases with age. However, the 1‐year follow‐up of Down's syndrome found that none of the ERPs measures predicted subsequent cognitive decline. The present study provides a novel characterization of electrophysiological markers of local and global predictive processes in Down's syndrome.