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Rex Motor Manufacturing Co. Ltd., Osborne Road, Earlsdon, Coventry.
Sold under names that included; Ast-Rex, Airex, Rexette, Rex-Remo and Rex-Simplex.
1901 Made the 'Mountaineer' motorcycle for the International Motor Car Co
1902 Enlarged their works and built a range of three and four wheel cars and their first motorcycle with a 247 cc four-stroke engine.
1902 August, Details of the 14-hp two-cylinder motor.
1903 The Rex design was changed and a 'beehive' silencer added, so that it was incorporated into the right side of the cylinder. Thus, the model had an unconventional exhaust and silencer. That year also brought the arrival of air-ducted engine cooling. A Rex was entered for the Paris-Madrid race, but failed to start.
1904 A combination tool and battery box was fitted between the seat tube, chain stays and rear mudguard on a machine with a 3.25 hp engine. Harold Williamson set a new End-to-End record, which he kept until 1908.
1905 July. Details of the Rexette two-cylinder car.
1906 Made the first telescopic forks, and several other innovations including rotary-valve engines
1906 Claimed 'the largest output of any motorcycle company in the world'
1907 Built the 'Blue Devil' 5 hp V-twin machine for Muriel Hind
1908 Rex were the first to angle the top tube downward to lower the riding position.
1910 Following further expansion, a new engine cradle was introduced. This replaced an outdated version that had been in use since 1902. They also produced 499cc two-stroke Rex Valveless with magneto ignition. This was eventually sold as the PMC.
1911 The Company fired the founders after a boardroom row and with them went a lot of the company’s prestige. Billy Williamson, who had been the Managing Director left and formed Williamson Motor Co. Harold Williamson became Sales Manager at Singer.
1912 Richard Lord (2) of the company married Muriel Hind
1912-1916 Various models were produced under the Rex-JAP name with many being built in the Rex works but sold by the Premier Motor Co of Birmingham. Gradually the range shrank and by 1916 only chain-driven, three-speed V-twins were produced. All production then stopped completely.
1912 Spennell's lists them at Osborne rd, Coventry and as motorcycle manufacturers 
1913-1917 For a list of the models and prices of motorcycles see the 1917 Red Book
1914 In voluntary liquidation. '...In the Matter of the REX MOTOR MANUFACTURING CO. Limited. (In Voluntary Liquidation.)...'
1920 A three model range appeared consisting of two 4hp singles and a 8hp V-twin - all with three speeds and chain-cum-belt transmission.
1936 Listed to be struck off