Observations of two quiescent filaments show oscillatory variations in Doppler shift and central intensity of the He I Solar 10830 Angstroms line. The oscillatory periods range from about 5 to 15 min. with dominant periods of 5, 9, and 16 min. The possibility that the oscillations are Alfven waves is discussed. The Doppler signals of the filament form fibril-like structures. The fibrils are all inclined at an angle of about ...