  We study the nature of electronic states in one-dimensional continuous models
with weak correlated disorder. Using a perturbative approach, we compute the
inverse localisation length (Lyapunov exponent) up to terms proportional to the
fourth power of the potential; this makes possible to analyse the
delocalisation transition which takes place when the disorder exhibits specific
long-range correlations. We find that the transition consists in a change of
the Lyapunov exponent, which switches from a quadratic to a quartic dependence
on the strength of the disorder. Within the framework of the fourth-order
approximation, we also discuss the different localisation properties which
distinguish Gaussian from non-Gaussian random potentials.
