Vibrational photon echo experiments were performed on the asymmetric CO stretching mode of tungsten hexacarbonyl in glassy dibutylphthalate as a function of temperature using sub-picosecond infrared pulses (1976 cm(-1)) from a flee electron laser. The echo decays display pronounced beats and are bi-exponential. The beats and bi-exponential decays arise because the bandwidth of the pulses exceed the vibrational anharmonicity, leading to the excitation and dephasing of a multilevel coherence. From the beat frequency, the anharmonicity is determined to be 14.7 cm(-1). From the bi-exponential decay components, the temperature-dependent vibrational dephasing of both the upsilon = 0 --> 1 and upsilon = 1 --> 2 transitions are determined.