Quantum coherence and its dephasing by coupling to a dissipative environment play an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions in the condensed phase. We have discussed nonlinear optical processes on a multi-state one-dimensional system with Morse potential surfaces in a dissipative environment. This was based on a numerical study using the multi-state quantum Fokker-Planck equation for a colored Gaussian-Markovian noise bath, which was expressed as a hierarchy of kinetic equations. This equation can treat strong system-bath interactions at a low temperature heat bath, where quantum effects play a major role. The approach applies to linear absorption measurements as well as four-wave mixing including pump-probe spectroscopy. Laser induced photodissociation and predissociation have been studied for the potential surfaces of Cs-2. We have calculated nuclear wave packets in Wigner representation and their monitoring by femtosecond pump-probe spectroscopy for various displacements of potentials and heat-bath parameters. Numerical calculations of probe absorption spectra for strong pump pulse are also presented and discussed. The results show dynamical Stark splitting, but, in contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperature their peaks have different heights even when the pump pulse is on resonance.