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you advance the throttle as much as possible without going into afterburner or basically the ability to hit mach in level flight without a/b
Plenty of older aircraft can do it, take this not particularly comprehensive list of aircraft capable of supercruising from wikipedia:

* SR-71 Blackbird
* Concorde
* Tupolev Tu-144
* English Electric Lightning
* F-104 Starfighter
* Eurofighter Typhoon
* F-16XL
* F-14A+
* F-22 Raptor
* YF-23 Black Widow II
* XB-70 Valkyrie
* Dassault Rafale
* F-4 Phantom II (Israeli "Super Phantom" variant)
* Mikoyan-Gurevich MiG-25
(B-58 could also supercruise apparently)

This except from this article on the F-104 provides some interesting reading on the subject.
Starfighter F-104
Many of the Century Series fighters could supercruise, though most of those just barely. (As a rule of thumb, any plane which can exceed Mach 2 with afterburner can probably exceed Mach 1 without.) Starfighters with the J79-19 engine can - at altitude - maintain about Mach 1.1 in level flight in military power (maximum throttle without afterburner). This isn't surprising when you realize that the J79 engine was vastly improved during the long production lifetime of the F-104, with later versions producing nearly as much thrust without afterburner as early models did with. (In his comments on the F-22, retired Colonel Everest Riccioni (one of three legendary "Fighter Mafia" mavericks who forced the Pentagon to produce the F-16, to improve U.S. air superiority, who flew 55 different types of military aircraft, and worked in the defense industry for 17 years managing aircraft programs, including the B-2 bomber) compared it unfavorably to the F-104-19 in several categories, including supercruise range.)

To give an idea of how far a Starfighter could go at supersonic speeds, an F-104A with no external stores could take off, climb to 20,000 meters, accelerate to Mach 2 and fly for fifteen minutes, and still have plenty of reserve for descent and landing. (Just be sure to bring your pressure suit along.) Adding wingtip tanks increased the fuel available with little effect on top speed, in spite of the drag they created. (Tanks and missiles on the wingtips also helped the plane turn tighter, since they acted as endplates on those stubby wings.) Later models had improved J79 engines with better fuel economy, plus increased internal tankage, so they could cruise supersonic for even longer. They also had more military (dry, or non-afterburning) thrust, making the Zipper's supercruise capability less marginal. Some F-104A aircraft were later modified to take the J79-19 engine, originally developed for the F-104S. Since the A was the slickest and lightest production version of the plane it had spectacular climb and acceleration with the new engine.

The top speed of most fighters - even today - is limited by thrust (the F-16 has a higher thrust-to-weight ratio than the Starfighter, but it also has a huge delta wing which is optimized for maneuvering and generating lift to carry large amounts of external stores, not for supersonic flight). The F-104 is generally restricted by heat in the compressor section of the engine and certain parts of the airframe. Early Starfighters could not exceed Mach 2.2 without potentially damaging the engine; on later models with the -19 engine this was increased to Mach 2.3. The canopy limit is around Mach 2.6. The airframe on late models is stable out to Mach 2.8. As top speed is approached in the F-104 the pilot must throttle back to keep from exceeding the safe limits, unlike almost any other plane*. One US Air Force pilot wrote that in his experience the F-104 was the only plane he had ever flown where even the squadron dog could exceed all the red lines. For comparison, the normal top speed of the F-15 is Mach 2.3, with a time-limited pursuit mode of Mach 2.6. It can do this carrying some missiles, but not with drop tanks. (Later models of the Eagle with improved engines may be able to.)

*My note: MiG-25 is also similar in this respect of having more thrust than it can use for top speed, the engines being limited to Mach 2.8 at which point delicate throttle use is required because at that speed it is very easy for the engines to get carried away and overspeed, which happened in the case of the infamous Mach 3.2 MiG-25 over Israel.
Only the P.1 and P.1A prototypes of the English Electric Lightning could super-cruise. The production Lightnings could not. The Lightning would, however, at some point during it's flight achieve a thrust-to-weight ratio equal to 1:1. But the F-15 was the first plane to achieve that on take-off, with full load.

Basically, supercruise is the ability to go beyond the speed of sound in level flight without the use of afterburners. It's just a coined term for a fast plane!

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