Ring laser gyroscopes, in which rotation is detected by the Sagnac effect between counterpropagating lasers, are in common use in navigation applications. The invention disclosed here uses an induced strong anomalous dispersion inside the ring laser cavities to create a group velocity of as much as 106 times greater than the vacuum speed of light, with a corresponding increase in gyroscope sensitivity; the resulting device is referred to as a Superluminal Ring Laser Gyroscope (SRLG). The invention disclosed here also incorporates an acceleration-sensing element that modifies the path length of the ring lasers in the gyroscope, the effects of which on the output of the gyroscope can be separated from those of rotation. The resulting composite device is a Superluminal Ring Laser Gyroscope/Accelerometer (SRLGA).