Abstract:This chapter deals with the theories of vibrational line profiles and anomalous (negative) frequency non-coincidence effects in condensed media. First, a novel approach to the line profile analysis is described. It is based on a new, flexible time-correlation function (TCF), which has an analytical counterpart in the frequency domain. Using this function one can fit vibrational line profiles obtaining dynamical information at the same time. Numerous applications of this TCF are considered, including analyses of both line profiles and dynamics. Second, direct methods of estimation of repulsion contributions to frequency shifts and non-coincidence effects are described, and model calculations enabling one to separate the contributions of repulsion and attraction forces resulting in frequency non-coincidences are presented