Naïve mouse embryonic stem (ES) cells can readily acquire specific fates, but the cellular and molecular processes that enable lineage specification are poorly characterised. Here we investigated progression from the ES cell ground state in adherent culture. We utilised down-regulation of Rex1::GFPd2 to track loss of ES cell identity. We found that cells that have newly down-regulated this reporter have acquired competence for germline induction. They can also be efficiently specified for different somatic lineages, responding more rapidly than naïve cells to inductive cues. Nodal is a candidate autocrine regulator of pluripotency. Abrogation of Nodal signalling did not substantially alter kinetics of exit from the ES cell state, but accelerated subsequent adoption of neural fate at the expense of other lineages. This effect was evident if Nodal was inhibited prior to extinction of ES cell identity. We suggest that Nodal is pivotal for non-neural competence in cells departing naïve pluripotency.