This paper explores potential of the decision tree method for tacking the on-line transient stability strategy of the Hydro-Québec power system. The specifics of this system are first described along with its very structure which makes transmission capacity strongly dependent on transient stability limits. Decision trees are then properly adjusted to this intricate real world problem, in particular by using composite attributes, decomposition of the problem into subproblems, and techniques able to reduce the number of dangerous (overoptimistic) diagnostics. Further, the resulting trees are compared with LIMSEL, i.e. the transient stability software presently used at Hydro-Québec; they are found able to provide indeed an interesting alternative thanks to their intrinsic assets. Finally, limitations of decision trees are discussed and the interest to combine them with other, complementary automatic learning approaches is suggested. This latter issue is explored in a companion paper