We study charge-transfer dynamics monitored by two-dimensional (2D) optical spectroscopy. The often used model consisting of two coupled diabatic electronic states in a single reaction coordinate is used to demonstrate the relation between the vibronic dynamics and the 2D-spectra. Within the employed wave-function approach, dissipation is included via a quantum-jump algorithm with explicit treatment of dephasing. States with long lifetimes which decay slowly due to the interaction with the environment are identified. Using filtered Fourier transforms, energy and time resolved information about the dissipative system dynamics can be obtained. (C) 2016 Elsevier B.V. All rights reserved.