Novel two-dimensional (2D) vibrational spectroscopies that are suitable for the investigation of the vibrational couplings of adsorbed molecules on surfaces or at interfaces are theoretically proposed. Depending on the sequence of the IR, Raman, and hyper-Raman transitions involved, there are seven distinctive nonlinear response functions associated with various 2D surface vibrational spectroscopies, which are either three- or five-wave-mixing processes. It is suggested that these novel techniques can be used to obtain information on the nonlinear coordinate dependencies of the dipole moment, polarizability, and hyperpolarizability as well as on the anharmonic couplings between any two vibrational degrees of freedom of adsorbed molecules.