In previous papers a stochastic model of the ageing process has been proposed. Some genetic parameters (redundance, repair) have been used to explain the observed differential predisposition to the process and family heredity. Because the process is basically due to effective random mutations, any individual of the population would be predisposed differently to ageing according to the structure of his/her genome. In the present paper, the previous model is generalized to take into account an additional genetic parameter, namely, the stability against random mutations, defined as the probability that a random mutation in a codon would produce no mutation in the corresponding protein. Estimation problems connected with the model are approached on the basis of twin data in maximum likelihood estimation as well as in bayesian framework. Some comparisons between the two methods are reported.