  We study the dynamics of fluctuations at the critical point for two
time-asymmetric version of the Curie-Weiss model for spin systems that, in the
macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the
macroscopic limit reflect the type of bifurcation, as they exhibit observables
whose fluctuations evolve at different time scales. The limiting dynamics of
fluctuations of slow observable is obtained via an averaging principle.
