  We consider the spatiotemporal evolution of a wave packet in disordered
nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of
nonlinearity all eigenstates are spatially localized with an upper bound on the
localization length (Anderson localization). Nonlinear terms in the equations
of motion destroy Anderson localization due to nonintegrability and
deterministic chaos. At least a finite part of an initially localized wave
packet will subdiffusively spread without limits. We analyze the details of
this spreading process. We compare the evolution of single site, single mode
and general finite size excitations, and study the statistics of detrapping
times. We investigate the properties of mode-mode resonances, which are
responsible for the incoherent delocalization process.
