We have carried out high-resolution photoemission experiments on two quasi-one-dimensional compounds: K0.3MoO3 and (TaSe4)2I. In both systems, a metal-insulator transition associated with a lattice distortion is reported. We show that the Fermi-step characteristic of a metallic phase is not observed above the Peierls temperature. As this Fermi step is always observed in higher-dimensional metals, we propose that this behavior results from the singular properties of one-dimensional systems and we suggest different mechanisms in order to explain this striking result.