Hope and Inquietudes in Nucleo-cosmochronology

Critical views are presented on some nucleo-cosmochronological questions. Progress has been made recently in the development of the 187Re-187Os cosmochronometry. From this, there is good hope for this clock to become of the highest quality for the nuclear dating of the Universe. The simultaneous observation of Th and U in ultra-metal-poor stars would also be a most interesting prospect. In contrast, a serious inquietude is expressed about the reliability of the chronometric attempts based on the classical 232Th-238U and 235U-238U pairs, as well as on the Th (without U) abundance determinations in ultra-metal poor stars.