We propose a flexible copula model to describe changes with a covariate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the generator of an Archimedean copula. Changes in the dependence structure with a covariate x are modelled by flexible regression of the spline coefficients on x. The performances and properties of the spline estimate of the reference generator and the abilities of these conditional models to approximate conditional copulas are studied through extensive simulations. Inference is made using Bayesian arguments with posterior distributions explored using importance sampling or adaptive Markov chain Monte Carlo algorithms. The modelling strategy is illustrated with the analysis of bivariate growth curve data. Copyright © 2014 John Wiley & Sons, Ltd.