The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies -absorption, emission, scattering, conductance, photofragmentation -applied to very varied systems -atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.Whenever a discrete state and a continuum state interact and radiative transitions are allowed from the ground state to both, an interference occurs that gives rise to the Fano lineshape [1][2][3][4]. In the presence of dissipative processes, it has been shown that the generalized Fano equation consisting of a standard Fano plus a Lorentzian term is [1, 2, 5-9]:where q = µ e /nπV µ c and = (ω L − ω e )/γ e , µ e is the transition dipole moment to the discrete excited state, µ c the transition dipole moment to the continuum, V the coupling of the discrete excited state to the continuum, n the density of states of the continuum, ω e is the energy of the discrete state relative to the ground state, ω L is the radiation field frequency, and γ e = nπV 2 is the linewidth of the excited state, induced by its coupling nV 2 to the continuum set of states. C is the weight of the Lorentzian term and is related to the dissipative processes [6][7][8][9][10]. Since its original inception, the 1961 paper has resulted in more than 8,000 citations testifying to its ubiquity in physics, chemistry and materials science. The first Fano profiles were observed more than 80 years ago in atomic spectra, including photoionization of atoms and photodissociation of small molecules [3,4]. The field of study was established around scattering processes where the phenomena of coupling to a thermal bath resulting in dissipation or decoherence is not important, except in a few cases, notably pressure broadening [11][12][13].The synthesis and control of matter at the nanoscale opened up the observation of Fano profiles to dissipative systems [14][15][16][17][18] which in turn spurred a renewed interest in theoretical descriptions that would solve the problem in open quantum systems [8][9][10][19][20][21], and correctly account for the relaxation. Consequent with this desire to measure dissipation, more sophisticated spectroscopies are to be invoked. 2D electronic spectroscopy (2DES) is arguably one of the best spectroscopies to measure decoherence and relaxation between states [22][23]...