Charge-density waves in one-dimensional conductors in the presence of electron- phonon and electron-electron interactions are investigated. The problem is mapped into the 2D sine-Gordon model. Using the renormalisation group results for the sine-Gordon model we find that in the critical region a ‘Peierls’ gap is opened up. The analytic form of this gap is of Kosterlitz-Thouless nature. In the adiabatic limit we find that the 'Peierls' gap depends on a non-universal exponent. These non-universal exponents are given by the line of fixed points of the XY model. © 1986 The Institute of Physics.