In this thesis, both time-resolved, nonlinear optical spectroscopy and linear spectroscopy are used to investigate the interactions and dynamics of elementary excitations in strongly correlated electron systems. In the first part, we investigate the renormalization of magnetic elementary excitations in the transition metal oxide Cr{sub 2}O{sub 3}. We have created a non-equilibrium population of antiferromagnetic spin waves and characterized its dynamics, using frequency- and time-resolved optical spectroscopy of the exciton-magnon transition. We observed a time-dependent pump-probe line shape, which results from excitation induced renormalization of the spin wave band structure. We present a model that reproduces the basic characteristics of the data, in which we postulate the optical nonlinearity to be dominated by interactions with long-wavelength spin waves, and the dynamics due to spin wave thermalization. Using linear spectroscopy, coherent third-harmonic generation and pump-probe experiments, we measured the optical properties of the charge-transfer (CT) gap exciton in Sr{sub 2}CuO{sub 2}Cl{sub 2}, an undoped model compound for high-temperature superconductors. A model is developed which explains the pronounced temperature dependence and newly observed Urbach tail in the linear absorption spectrum by a strong, phonon-mediated coupling between the charge-transfer exciton and ligand field excitations of the Cu atoms. The third-order nonlinear optical susceptibility …