  We introduce tame abstract elementary classes as a generalization of all
cases of abstract elementary classes that are known to permit development of
stability-like theory. In this paper we explore stability results in this
context. We assume that $\K$ is a tame abstract elementary class satisfying the
amalgamation property with no maximal model. The main results include:
  (1) Galois-stability above the Hanf number implies that \kappa(K) is less
than the Hanf number. Where \kappa(K) is the parallel of \kapppa(T) for f.o. T.
  (2) We use (1) to construct Morley sequences (for non-splitting) improving
previous results of Shelah (from Sh394) and Grossberg & Lessmann.
  (3) We obtain a partial stability-spectrum theorem for classes categorical
above the Hanf number.
