Adolf Busemann had proposed swept wings as early as 1935; Messerschmitt researched the topic from 1940. In April 1941, Busemann proposed fitting a 35° swept wing (Pfeilflügel II, literally "arrow wing II") to the M e 262, the same wing-sweep angle later used on both the American F-86 Sabre and Soviet Mikoyan-Gurevich MiG-15 fighter jets. Though this was not implemented, he continued with the projected HG II and HG III (Hochgeschwindigkeit, "high-speed") derivatives in 1944, designed with a 35° and 45° wing sweep, respectively.

Interest in high-speed flight, which led him to initiate work on swept wings starting in 1940, is evident from the advanced developments Messerschmitt had on his drawing board in 1944. While the Me 262 V9 Hochgeschwindigkeit I (HG I) flight-tested in 1944 had only small changes compared to combat aircraft, most notably a low-profile canopy—tried as the Rennkabine (literally "racing cabin") on the ninth Me 262 prototype for a short time—to reduce drag, the HG II and HG III designs were far more radical. The projected HG II combined the low-drag canopy with a 35° wing sweep and a V-tail (butterfly tail). The HG III had a conventional tail, but a 45° wing sweep and turbines embedded in the wing roots.

Messerschmitt also conducted a series of flight tests with the series production Me 262. Dive tests determined that the Me 262 went out of control in a dive at Mach 0.86, and that higher Mach numbers would cause a nose-down trim that the pilot could not counter. The resulting steepening of the dive would lead to even higher speeds and the airframe would disintegrate from excessive negative g loads.

The HG series of Me 262 derivatives was believed capable of reaching transonic Mach numbers in level flight, with the top speed of the HG III being projected as Mach 0.96 at 6,000 m (20,000 ft) altitude. After the war, the Royal Aircraft Establishment, at that time one of the leading institutions in high-speed research, re-tested the Me 262 to help with British attempts at exceeding Mach 1. The RAE achieved speeds of up to Mach 0.84 and confirmed the results from the Messerschmitt dive-tests. The Soviets ran similar tests.

After Willy Messerschmitt's death in 1978, the former Me 262 pilot Hans Guido Mutke claimed to have exceeded Mach 1 on 9 April 1945 in a Me 262 in a "straight-down" 90° dive. This claim relies solely on Mutke's memory of the incident, which recalls effects other Me 262 pilots observed below the speed of sound at high indicated airspeed, but with no altitude reading required to determine the speed. The pitot tube used to measure airspeed in aircraft can give falsely elevated readings as the pressure builds up inside the tube at high speeds. The Me 262 wing had only a slight sweep, incorporated for trim (center of gravity) reasons and likely would have suffered structural failure due to divergence at high transonic speeds. One airframe—the aforementioned Me 262 V9, Werknummer 130 004, with Stammkennzeichen of VI+AD, was prepared as the HG I test airframe with the low-profile Rennkabine racing-canopy and may have achieved an unofficial record speed for a turbojet-powered aircraft of 975 km/h (606 mph), altitude unspecified, even with the recorded wartime airspeed record being set on 6 July 1944, by another Messerschmitt design—the Me 163B V18 rocket fighter setting a 1,130 km/h (700 mph) record, but landing with a nearly disintegrated rudder surface.

Sources:
Gunston, Bill & Wood, Tony - Hitler's Luftwaffe, 1977, Salamander Books Ltd., London
Wikipedia - ME 262