  We investigate the critical slowing down of the topological modes using local
updating algorithms in lattice 2-d CP^(N-1) models. We show that the
topological modes experience a critical slowing down that is much more severe
than the one of the quasi-Gaussian modes relevant to the magnetic
susceptibility, which is characterized by $\tau_{\rm mag} \sim \xi^z$ with
$z\approx 2$. We argue that this may be a general feature of Monte Carlo
simulations of lattice theories with non-trivial topological properties, such
as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N)
lattice gauge theories.
