The usual view of exciton-exciton annihilation (EEA) processes in molecular aggregates is based on locally excited states of the monomer units. However, the corresponding localized configurations can only be assumed if the system is in a coherent superposition of eigenstates, i.e., a wave packet. We study a molecular dimer and focus on the characterization of EEA by a wave packet motion induced in the system by ultrashort pulse excitation. Here, coherences that appear are destroyed by dissipation processes. We discuss the influence of interband and intraband relaxation on the dynamics. The states that participate in the annihilation process are directly accessible by fifth-order optical two-dimensional spectroscopy. Such spectra are calculated, and spectral features are related to the annihilation process.