Huntington's chorea is a late onset disease of the nervous system whose mode of inheritance conforms to the autosomal dominant model. The present paper shows how the problem of estimating the distribution of age at onset of the disease can be dealt with as an incomplete data problem via the EM algorithm, both in the parametric and non-parametric setting. In this way it is possible to take into account not only the heterozygotes in the population under study who are manifestly affected, but also those who are apparently unaffected. The estimation of the distribution of age at onset of the disease is required for estimating the posterior probability of heterozygosity of the individual at risk using Bayes' theorem. The proposed approach was applied to data derived from a survey carried out on the population of Latium, Italy.