  Let K be an abstract elementary classes which has arbitrarily large models
and satisfies the amalgamation and joint embedding properties.
  Theorem 1. Suppose K is \chi-tame. If K is categorical in some \lambda^+
>LS(K) then it is categorical in all \mu\geq (\lambda+\chi)^+.
  Theorem 2. If K is LS(K)-tame and is categorical both in LS(K) and in LS(K)^+
then K is categorical in all \mu\geq LS(K).
