  We study the phase transition in generalized chiral or Stiefel's models using
Monte Carlo simulations. These models are characterized by a breakdown of
symmetry O(N)/O(N-P). We show that the phase transition is clearly first order
for N >= 3 when P=N and P=N-1, contrary to predictions based on the
Renormalization Group in 4-\epsilon expansion but in agreement with a recent
non perturbative Renormalization Group approach.
