Theory and experimental data are presented which illustrate a new method for performing two-dimensional vibrational spectroscopy using ultrafast pulsed infrared lasers, called vibrational echo spectroscopy (VES). The VES technique can generate a vibrational spectrum with background suppression using the nonlinear vibrational echo pulse sequence. The vibrational echo pulse sequence is used with the delay between the excitation pulses fixed while the excitation wavelength is varied. A detailed theory of VES is presented which calculates the full third order nonlinear polarization including rephasing and nonrephasing diagrams. Finite width laser pulses are used and the calculations are performed for a model spectrum with two or more peaks. Two mechanisms that can result in background and peak suppression are illustrated. The mechanisms are based on differences in homogeneous dephasing times (T-2) or transition dipole matrix element magnitudes. Although the VES line shape differs from the absorption line shape, it is possible to recover the absorption line shape from the VES. The method is demonstrated experimentally on the vibrational mode of CO (center at 1945 cm(-1)) bound to the active site of the protein myoglobin (Mb-CO). The protein and solvent produce a large absorption background while the VES spectrum of Mb-CO is background free. Calculations are able to reproduce the experimental Mb-CO VES line shape.