Abstract: By using the theory of fracture mechanics and the theory of wave propagation in rheo-logical medium the sources and propagation characteristics of long-period deformational waves of the earth before large earthquakes are studied. On the basis of theoretical work, the observational data of short-term and imminent precursors before many strong and moderate earthquakes occurred in China are analyzed, and among them some kinds of precursors which could be related to long-period deformational waves are recognized.Considering brittle fracture and stick-slip as two main types of earthquake mechanism, it is suggested that both pre-slips before stick-slips and crack propagation before rupture may be the sources of long-period deformational waves a large earthquake of which the latter has been emphasized, in our discussion.Taking a complex rheological model of crustal medium, some general characteristics of propagation of long-period deformational waves have been studied and solutions of corresponding dynamic problems for the propagation of long-period waves caused by the two given types of sources were obtained theoreticallyThen, the observational data of short-term and imminent precursors before a series of large earthquakes were analyzed, especially, the precursors before the Tangshan (M=7.8) and Liyang (M =6.0) earthquakes were studied in detail. Among the precursors analyzed, some oscillation-type and step-type changes of precursors can be observed by using automatic recordings of underground water level, tiltmeter and the tidegauge measurements, that might be closely correlated with the long-period deformational waves studied here theoretically.Based on the theoretical and practical results obtained, some general characteristics of short-term and imminent precursors as given rise by the long-period deformational waves have been summarized. They are of the velocity of wave propagation, amplitude attenuation, type of vibration, waveform change, intensity distribution, period range, time of precursory appearance before earthquake and maximum distance of propagation.In conclusion, the methods for observation and analysis of long-period deformational waves and their application to earthquake prediction particularly short-term and imminent prediction and to the study of earthquake source process are briefly discussed.