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Any listening task, from sound recognition to sound-based communication, rests on auditory memory which is known to decline in healthy ageing. However, how this decline maps onto multiple components and stages of auditory memory remains poorly characterised. In an online unsupervised longitudinal study, we tested ageing effects on implicit auditory memory for rapid tone patterns. The test required participants (younger, aged 20-30, and older adults aged 60-70) to quickly respond to rapid regularly repeating patterns emerging from random sequences. Patterns were novel in most trials (REGn), but unbeknownst to the participants, a few distinct patterns reoccurred identically throughout the sessions (REGr). After correcting for processing speed, the response times (RT) to REGn should reflect the information held in echoic and short-term memory before detecting the pattern; long-term memory formation and retention should be reflected by the RT advantage (RTA) to REGr vs REGn which is expected to grow with exposure. Older participants were slower than younger adults in detecting REGn and exhibited a smaller RTA to REGr. Computational simulations using a model of auditory sequence memory indicated that these effects reflect age-related limitations both in early and long-term memory stages. In contrast to ageing-related accelerated forgetting of verbal material, here older adults maintained stable memory traces for REGr patterns up to 6 months after the first exposure. The results demonstrate that ageing is associated with reduced short-term memory and long-term memory formation for tone patterns, but not with forgetting, even over surprisingly long timescales.