  A higher-order analysis of the evolution of cosmological perturbations in a
Friedman universe is given by using the PMF method. The essence of the PMF
approach is to choose a gauge where all fluctuations of the density, the
pressure, and the four-velocity vanish. In that gauge, even in higher orders,
the perturbation field equations simplify considerably; they can be decoupled
and - for simple equations of state - also be solved analytically. We give the
solution for the dust universe up to third order. Comparison of these solutions
strongly supports the conjecture that in general instable perturbations grow
much faster than they do according to the first-order analysis. However,
perturbations with very large spatial extension behave differently; they grow
only moderatly. Thus, an upper boundary of the region of instability seems to
exist.
