  In the absence of nonlinearity all eigenmodes of a chain with disorder are
spatially localized (Anderson localization). The width of the eigenvalue
spectrum, and the average eigenvalue spacing inside the localization volume,
set two frequency scales. An initially localized wavepacket spreads in the
presence of nonlinearity. Nonlinearity introduces frequency shifts, which
define three different evolution outcomes: i) localization as a transient, with
subsequent subdiffusion; ii) the absence of the transient, and immediate
subdiffusion; iii) selftrapping of a part of the packet, and subdiffusion of
the remainder. The subdiffusive spreading is due to a finite number of packet
modes being resonant. This number does not change on average, and depends only
on the disorder strength. Spreading is due to corresponding weak chaos inside
the packet, which slowly heats the cold exterior. The second moment of the
packet is increasing as $t^{\alpha}$. We find $\alpha=1/3$.
