When dynamics of a system strongly coupled to a white-noise environment is overdamped, in linear spectroscopy, the spectrum is observed as one peak near zero vibrational frequency. We found, however, that if the noise induced by the environment is colored and its correlation time is long, there is an additional peak at a frequency different from the system. We study the multi-dimensional spectrum, to observe the interplay between the overdamped motion and the weakly damped motion induced by the colored noise. Finally, we discuss the connection between the peak due to the colored noise and the Boson peak found in glass materials and supercooled liquids. (C) 2002 Elsevier Science B.V. All rights reserved.