The history of F-Zero is separated in two diferent chronologies. The first one is contains most of the games in the series, while the second one follows the history of the anime.
F-Zero begins in the year 2560 where human race's countless encounters with alien life forms throughout the universe greatly expanded Earth's social framework resulting in trade, technology transfer, and cultural interchange are carried out on an interplanetary basis. An association of wealthy space merchants created the "F-Zero Grand Prix", in an attempt to add some excitement to their opulent lifestyles. When the first race was held, people were angered at the brutality of the competition, due to the various obstacles and traps along the raceway. As time passed, however, they became accustomed to these dangers, and even began to demand more excitement and danger in the races. Winning the F-Zero championship soon became the highest claim to fame in the universe. This period of time is called the "old-school" F-Zero days where the rules seemed non-existent in F-Zero X.
F-Zero X's storyline starts after the seven-year suspension of Grand Prix races due to the Horrific Grand Finale. The game explains the "Horrific Grand Finale" was a violent and fiery accident that burnt fourteen drivers to death, including Sterling LaVaughn during the old days of F-Zero. A racer named Super Arrow escaped unscathed as the only survivor. No racing was allowed by the Federation after the crash; despite the F-Zero racing prohibition, the sport went underground where many racers went to hone their skills in secret. The crash ushered in the establishment of the "F-Zero Racing Academy", after a speech, by Super Arrow to the Federation Congress, which helped to lift the ban. The fictional competition was brought back with the rules and regulations revised
F-Zero GX does not mention the Grand Finale event, but instead the game states Sterling LaVaughn was racing during the F-Max era and the F-Zero Grand Prix was suspended four years ago. This game states the character Mighty Gazelle was injured in the huge accident four years ago. However, the Nintendo 64 game mentions that Mighty Gazelle's accident and the accident that suspended the Grand Prix were two separate events.
F-Zero: Maximum Velocity takes place twenty-five years after the SNES title in the year 2585. Players race against the descendants of the original F-Zero racers. Maximum Velocity is considered a reboot continuity to the rest of the home console titles since the game has made no indication of the safety revisions carried forth after the huge accident, in fact it states just like the original F-Zero game, the extreme danger involved when participating in those races.
This chronology follows the same characters, but with different backgrounds. The games on this continuity follows the Anime history line. In this continuity the events occur following the order of F-Zero: GP Legend and its sequel F-Zero Climax.
Its not clear where the BS F-Zero Grand Prix games fit in the continuity. But its possible that they happen during the time the races where suspended, and these games are the secret races. It's even possible that the racers in this game were the four racers from the first game using different machines to not be recognized.
Some especulate tha the game Mach Rider is a spiritual prequel to the F-Zero series. This happens because the similarities betwen the universes of the games, both happening in a distant future, and similarities betwen Captain Falcon, and the protagonist of Mach Rider. It may be in fact the F-Max Grand Prix.