High-resolution angle-resolved (ARPES) photoemission in the quasi-one dimensional (1D) Peierls systems (TaSe4)(2)I and K0.3MoO3 reveals spectral features with clear 1D character. Their dispersion and polarization dependence is consistent with open Fermi surfaces and with the symmetry properties of the lattice. However the measured spectral lineshapes are unusual in various respects, as shown also by a comparison with the quasiparticle spectra of a 'good' metal. A consistent description of the normal metallic phase and of the low-temperature insulating phases is possible within a polaronic scenario, where the carriers are strongly renormalized by the interaction with the lattice and the spectrum is largely incoherent. The quasiparticle signatures are hidden at the spectral leading edge.