Summary: In this paper, harmonic retrieval is addressed under the standard assumption of observations corrupted by an additive white Gaussian noise but also in the presence of hard clipped observations. A Bayesian approach to solve these problems is proposed. Bayesian models are first presented that allow us to define posterior distributions on the parameter space. All Bayesian inference is then based on these distributions. Unfortunately a direct estimation of these distributions and of their features requires evaluation of some complicated high-dimensional integrals. Efficient stochastic algorithms based on Markov chain Monte Carlo methods are presented here to perform Bayesian computation. In simulation on synthetic and real data sets, these algorithms allow the estimation of the unknown parameters in difficult conditions.