  We study the spreading of an initially localized wavepacket in two nonlinear
chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with
disorder. Previous studies suggest that there are many initial conditions such
that the second moment of the norm and energy density distributions diverge as
a function of time. We find that the participation number of a wavepacket does
not diverge simultaneously. We prove this result analytically for
norm-conserving models and strong enough nonlinearity. After long times the
dynamical state consists of a distribution of nondecaying yet interacting
normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this
result holds for any initially localized wavepacket, a limit profile for the
norm/energy distribution with infinite second moment should exist in all cases
which rules out the possibility of slow energy diffusion (subdiffusion). This
limit profile could be a quasiperiodic solution (KAM torus).
