  This study provides new results about the probabilistic behaviour of a class
of Euclidean algorithms: the asymptotic distribution of a whole class of
cost-parameters associated to these algorithms is normal. For the cost
corresponding to the number of steps Hensley already has proved a Local Limit
Theorem; we give a new proof, and extend his result to other euclidean
algorithms and to a large class of digit costs, obtaining a faster, optimal,
rate of convergence. The paper is based on the dynamical systems methodology,
and the main tool is the transfer operator. In particular, we use recent
results of Dolgopyat.
