  Strongly damped Doppler shift oscillations are observed frequently associated
with flarelike events in hot coronal loops. In this paper, a review of the
observed properties and the theoretical modeling is presented. Statistical
measurements of physical parameters (period, decay time, and amplitude) have
been obtained based on a large number of events observed by SOHO/SUMER and
Yohkoh/BCS. Several pieces of evidence are found to support their
interpretation in terms of the fundamental standing longitudinal slow mode. The
high excitation rate of these oscillations in small- or micro-flares suggest
that the slow mode waves are a natural response of the coronal plasma to
impulsive heating in closed magnetic structure. The strong damping and the
rapid excitation of the observed waves are two major aspects of the waves that
are poorly understood, and are the main subject of theoretical modeling. The
slow waves are found mainly damped by thermal conduction and viscosity in hot
coronal loops. The mode coupling seems to play an important role in rapid
excitation of the standing slow mode. Several seismology applications such as
determination of the magnetic field, temperature, and density in coronal loops
are demonstrated. Further, some open issues are discussed.
