Neanderthals lived until 28,000 years ago in Spain, so they were killed off by the "flood" of Homo that started 40,000 years ago. And Homo's weren't dominant in Europe until after this time ( 28,000 years ago) because almost no modern human skeletons have been found in Europe prior to 30,000 years ago.
The Neandertals’ last bastion appeared to be the Iberian Peninsula, where fossils from a Spanish site called Zafarraya have been dated to 32,000 years ago and tools attributed to Neandertals have been dated to around 28,000 years ago. Fred H. Smith, The Fate of the Neandertals, Scientific American April 2000, p. 106
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