The Lava mouse (Malpaisomys insularis), and the Canarian shrew (Crocidura canariensis) are endemic of the Eastern Canary Islands and islets. The former is extinct while Canarian shrew survives in the two main islands and two islets. In order to provide insights regarding causes and processes contributing to the extinction of these endemic mammals: (i) we established last occurrence dates for Lava mouse, and first records for two exotic species – House mouse (Mus musculus) and Black rat (Rattus rattus) – through direct 14C AMS dating of collagen from bones; (ii) we analysed recent material from Barn owl (Tyto alba gracilirostris) roosting sites to evaluate its impact on Canarian shrew in the presence of introduced rodents. The new data strongly suggest that the extinction of Lava mouse was the result of an accumulative process of independent disappearances (or ‘local extinctions’) affecting the isolated populations. The timing of the introduction of the Black rat on the main islands (before Middle Age European contact in Lanzarote and after Middle Age European contact in Fuerteventura) matches with the last occurrence dates for the presence of Lava mouse on these islands, and are very probably their cause. The losses of these Lava mouse populations occurred in an asynchronous way, spreading across at least six centuries. On small islands, hyperpredation emerges as the most plausible process to explain the disappearance of the Lava mouse in the absence of rat populations, although stochastic processes can not be definitively excluded.