We propose an exciton model for the peripheral plant light-harvesting complex LHCII that allows us to explain the absorption (OD) and linear dichroism (LD) spectra, the superradiance (SR), the pump-probe transient absorption (TA), the three-pulse photon echo peak shift (3PEPS), and transient grating (TG) kinetics at different excitation wavelengths. To calculate the nonlinear response we used the Liouville equation for the density matrix, expanded up to the third order with respect to the external field, with the Redfield relaxation superoperator in the exciton eigenstate basis. We found a few configurations of the antenna, with specific chlorophyll (Chl) a/b identities, orientations, and site energies, that allowed a simultaneous fit of these data while taking into account the excitonic interactions, the static disorder, and weak exciton-phonon coupling which induced dephasing and relaxation (energy transfer) between the exciton states. The spectral density of the exciton-phonon coupling adjusted from the fit allowed us to determine the time scales and pathways of energy transfer in LHCII. We find that the intraband (Chl b-->Chl b and Chl a-->Chl a) energy-transfer dynamics includes sub-picosecond (250-600 fs) exciton relaxation within dimeric or, in the Chl a band, more complicated clusters, sub-picosecond (600-800 fs) hopping between spatially separated clusters (in the a band), and "slow" (picosecond) migration between localized states. The interband (Chl b-->Chl a) transfer is characterized by the presence of very fast channels, the fastest taking only 120 fs, which connect both localized and dimeric b states with the a band. The overall relaxation/migration dynamics can be directly viewed by means of the time-dependent density matrix in the exciton and site representation. The latter representation allows us to visualize the time-dependent degree of delocalization. While the individual exciton states can be delocalized over 2-2.5 molecules in the Chl a region, thermal mixing results in a coherence size of 1.4-1.8 for the steady-state wave packet at room temperature. Altogether, we conclude that the experimentally determined dynamic and static properties of LHCII can be simulated very well on the basis of the proposed excitonic model.