They saw themselves as "el tercer grande". Before Atletico Madrid's La Liga win 2013-14, the previous team from outside Spain's top two of Real Madrid and Barcelona to claim the Primera Division was Valencia, in 2002 and 2004. They were the nation's third big club.
As well as those triumphs, the Mestalla-based side also reached back-to-back Champions League finals in 2000 and 2001, losing to Los Blancos and then to Bayern Munich. And in 2004, they won the UEFA Cup. Times were good.
Even a poor season under Ronald Koeman in 2007-08 ended in Valencia winning the Copa del Rey and, with Unai Emery as coach, Los Che finished in third place in the Primera Division for three successive seasons between 2010 and 2012.
Fans, however, were not satisfied as big-name players left the club one after another, with Juan Mata, David Silva and David Villa all departing. And despite the funds brought in, huge debts meant Valencia were forced to leave their new stadium only half-built.
A return to the Champions League in 2015 following a takeover provided new impetus, but that turned out to be another false dawn and the following season, coach Nuno was gone. In his place came Gary Neville, with no top-level experience, and the Englishman proved a disaster. He lost 7-0 to Barca and took the club from the Champions League to the brink of relegation.
Recovery has taken time. A 12th-placed finish in 2015-16 was followed by a repeat of that position last season and Valencia were no longer seen as a top team in Spain.
In fact, when Emery moved from Sevilla to Paris Saint-Germain, Valencia-based sports paper SuperDeporte was widely ridiculed for their headline: "Five years on, Emery is about to join another grande". The Mestalla outfit had fought relegation while Sevilla had just won the Europa League three times in a row.
But now Valencia are back. After nine rounds of La Liga, Los Che lie in second place with 21 points and remain unbeaten (along with leaders Barcelona and Atletico, in fourth). And this time, it looks like they are set to stick around at the top of the table.
Coach Marcelino Garcia Toral has been key to their success. The Asturian has had success wherever he has been, taking Recreativo Huelva into La Liga and securing an eighth-placed finish with the Andalusians, securing promotion amid a crisis with Zaragoza, steering Racing Santander to their best-ever placing of seventh in the Primera Division and enjoying further success with Villarreal, leaving the Yellow Submarine in the Champions League before his surprise sacking last year.
Marcelino's obsession with diet has seen Valencia's players subjected to a strict regime and midfielder Dani Parejo admitted this week: "I have lost five and a half kilos since he has been here". And he added: "It's hard at first, you go through a bad time, you're hungry, but your body adapts. Now I feel more agile and faster."
Parejo has been a revelation in central midfield this season, but the 28-year-old had actually made the decision to leave Valencia at the end of the last season. He stayed, however, when he found out Marcelino was joining the club. "I knew that we would do well with Marcelino," he said. "Because of the way we learn, the way we train every day, the way he prepares matches."
It is not only Parejo who has been transformed by the arrival of Marcelino. Many of the players who under-performed last season, including Jose Luis Gaya, Ezequiel Garay, Martin Montoya, Rodrigo and Simone Zaza, have been excellent. The Italian striker, a flop at West Ham and so disappointing at Valencia in 2016-17, won the award for Player of the Month in September and has scored more in La Liga (eight in nine games) than anyone else apart from Lionel Messi (11 in nine).
On top of that, the summer signings have all done well. Following high-profile disappointments in recent seasons such as Alvaro Negredo and Nani, Marcelino had a big say in the arrivals this time around and they have delivered.
Midfielder Geoffrey Kondogbia has slotted in seamlessly after a difficult spell at Inter, while goalkeeper Neto has made sure nobody now misses Diego Alves, and Gabriel Paulista has impressed at the back. "Marcelino told me he was going to change everything at Valencia and he has been good to his word," the former Villarreal and Arsenal defender said.
Colombia international Jeison Murillo has also done well since arriving on loan in the summer from Inter, but the greatest of them all has been Portuguese starlet Goncalo Guedes, who moved from PSG on a year-long deal and has already made his mark with some scintillating displays.
The 20-year-old's best game of all came in the 4-0 win at home to Sevilla at the weekend, when he struck two goals, including one stunning strike as he raced forward and cracked an unstoppable drive in off the crossbar.
That result, along with the team's 2-2 draw at the Bernabeu and their unbeaten start to La Liga, has convinced some supporters that even a title tilt is possible this time.
And although that maybe a step to far, there is no doubt that after some turbulent times, Valencia are back where they belong - challenging to be considered as Spain's third great club.