A supercharger for an internal combustion engine having at least one combustion chamber for accommodating a mass of air and fuel operable to supply a mass of air to the combustion chamber of the engine according to the mass of air requirements of the engine for a given power output of the engine, the supercharger comprising a housing having opposite first and second ends, a bore providing a first chamber and a second chamber, an air mass exit opening and an air mass bypass passage, said second chamber and air mass bypass passage having a common air mass bypass opening for allowing air to flow from the second chamber into the air mass bypass passage, a first end member connected to the first end of the housing, said first end member having an air mass inlet open to said first and second chambers (56,54), a second end member connected to the second end of the housing, a first rotor located in the first chamber rotatably mounted on the first and second end members (39,38), a second rotor located in the second chamber rotatably mounted on the first and second end members (39,38), a shuttle (87,487) located in the air mass bypass passage, said shuttle (87,487) having a movable body (108,208,408) to selectively close and open the air mass bypass opening for controlling the mass of compressed air directed to the engine and a mass of uncompressed air flowing from the second chamber into the air mass bypass passage, an actuator (88,89,109) operable to control a drive mechanism (88,109) to regulate the position of the shuttle (87,487) relative to the air mass bypass opening for controlling the mass of compressed air directed to the engine according to the power requirements of the engine, and a controller for providing command signals for operating the actuator (88,89,109) for moving the shuttle (87,487) between the open and closed positions relative to the air mass bypass opening for regulating the amount of the mass of compressed air introduced into the combustion chamber of the engine, characterized by: rails (143,148,243,248,343,348,443,448,562,563) projected into the air mass bypass passage, said rails (143,148,243,248,343,348,443,448,562,563) being joined to the housing and extended partly along the length of the air mass bypass passage, each of said rails (143,148,243,248,343,348,443,448,562,563) includes a first linear surface (146,151,246,251,346,351,567,565) and a second linear surface (147,152,247,252,347,352,568,566) located in planes that converge inwardly into the air mass bypass passage, and a plurality of rollers (123,124,126,131,132,133,134,136,137,223,224,236,324,331,333,336,424,431,433,436, 524,531,533,536) rotatably mounted on the movable body (108,408) of the shuttle (87,487) engageable with the rails (143,148,243,248,343,348,443,448,563,563) to movably support the shuttle (87,487) on the rails (143,148,243,248,343,348,443,448,562,563) for movement along the rails (143,148,243,248,343,348,443,448,562,563), the plurality of rollers (123,124,126,131,132,133,134,136,137,223,224,231,236,324,331,333,336,424,431,433, 436,524,531,533,536) comprise first rollers (124,133,224,233,324,333,424,433,524,533) located in engagement with the first linear surfaces (146,151,246,251,346,351,567,565) and second rollers (131,136,231,236,331,336,431,436,531,536) located in engagement with the second linear surfaces (147,152,247,252,347,352,568,562), the drive mechanism (88,109) operatively connected to the movable body (108,408) of the shuttle (87,487) for moving the shuttle (87,487) along the rails (143,148,243,248,343,348,443,448,563,563) between open and closed positions relative to the air mass bypass opening for controlling the mass of compressed air directed to the air mass exit opening and a mass of uncompressed air flowing through the air mass bypass opening. rails (143,148,243,248,343,348,443,448,562,563) projected into the air mass bypass passage, said rails (143,148,243,248,343,348,443,448,562,563) being joined to the housing and extended partly along the length of the air mass bypass passage, each of said rails (143,148,243,248,343,348,443,448,562,563) includes a first linear surface (146,151,246,251,346,351,567,565) and a second linear surface (147,152,247,252,347,352,568,566) located in planes that converge inwardly into the air mass bypass passage, and a plurality of rollers (123,124,126,131,132,133,134,136,137,223,224,236,324,331,333,336,424,431,433,436, 524,531,533,536) rotatably mounted on the movable body (108,408) of the shuttle (87,487) engageable with the rails (143,148,243,248,343,348,443,448,563,563) to movably support the shuttle (87,487) on the rails (143,148,243,248,343,348,443,448,562,563) for movement along the rails (143,148,243,248,343,348,443,448,562,563), the plurality of rollers (123,124,126,131,132,133,134,136,137,223,224,231,236,324,331,333,336,424,431,433, 436,524,531,533,536) comprise first rollers (124,133,224,233,324,333,424,433,524,533) located in engagement with the first linear surfaces (146,151,246,251,346,351,567,565) and second rollers (131,136,231,236,331,336,431,436,531,536) located in engagement with the second linear surfaces (147,152,247,252,347,352,568,562), the drive mechanism (88,109) operatively connected to the movable body (108,408) of the shuttle (87,487) for moving the shuttle (87,487) along the rails (143,148,243,248,343,348,443,448,563,563) between open and closed positions relative to the air mass bypass opening for controlling the mass of compressed air directed to the air mass exit opening and a mass of uncompressed air flowing through the air mass bypass opening.