The cognitive neuroscience of second language acquisition has been described as being associated with ＇excitement＇ and a ＇ sense of momentum＇ （Indefrey and Gullberg 2006 ： 7）. This article recognizes the enormous potential of the neuroscientific contribution to second language research, but it also points to problems and uncertainties which currently attend neurolinguistics. The article makes some comments in respect of some particular neurolinguistic studies relating to the over-interpretation of evidence, the failure to design studies in such a way as to take account of key variables, and the ignoring of facts about language that have been established for decades. The essential point of the article is that, if neuroscientific research is to be integrated into second language acquisition research, it has to operate on the basis of the same ground-rules as more ＇traditional＇ research--specifically with reference to： the acknowledgment of methodological and technical limitations, the restriction of conclusions to what is licensed by the data, controlling for possible confounding variables, and the incorporation of established linguistic and psycholinguistic facts into the analysis of findings.