HolaA fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order effi-ciency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented.