Barcelona's 2-1 loss at Ajax Amsterdam in the Champions League last week was down to a lack of intensity while Sunday's 1-0 reverse at Athletic Bilbao in La Liga exposed their relative physical frailty.
Leeds reach Championship play-offs final with 4-0 win over Norwich
In other matches, super-sub Messi helped Barca romp past Atletico
Barcelona followed up Saturday's win over Real Madrid with another victory when Alexis Sanchez set the champions on their way to a 3-0 success at Celta Vigo on Tuesday that put them four points clear at the top of La Liga.
La Liga players dominate this year's Best Player in Europe shortlist, announced by the continent's governing body UEFA on Monday, with seven of the top 10 contenders for the prestigious award currently plying their trade in Spain.
The win took second-placed Real to 62 points after 29 games, two behind champions Barca who beat Leganes 2-0 on Tuesday.
Second-half strikes by Federico Valverde, Brahim Diaz and Endrick gave feeble Real Madrid an unconvincing 3-0 win over lowly Real Valladolid.
Lionel Messi created a goal and scored another as Barcelona came from behind to beat struggling Rayo Vallecano 3-1 at home on Saturday and stay seven points clear at the top of La Liga.
"We are really pleased and we just have to enjoy it," Celta defender Gustavo Cabral told Spanish television.
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AC Milan will have to be perfect defensively when they host Premier League side Liverpool in their Champions League opener at San Siro, manager Paulo Fonseca said on Monday.
Beat Real Madrid's unbeaten run in the 1988-89 season, and thump Rayo Vallecano 5-1
Atletico Madrid made a typically aggressive start to lay the foundations for a 2-0 victory at home.
Barcelona's bid for a fifth La Liga title in six years suffered a surprise setback when the champions crashed to a 1-0 defeat at lowly Real Valladolid on Saturday.
Gareth Bale marked his return to action after a long injury layoff by sealing a 2-0 victory for Real Madrid over Espanyol on Saturday to provisionally stretch Zinedine Zidane's side's lead at the top of La Liga to three points.
Karim Benzema netted a second-half hat-trick as Real Madrid got back to winning ways with a 3-0 victory over Athletic Bilbao in La Liga on Sunday.
Atletico Madrid's La Liga title challenge took a nosedive when they slumped to a shock 3-0 defeat at Osasuna on Sunday, leaving Real Madrid three points clear at the top.
Two goals from Luis Diaz and one from Mohamed Salah helped Liverpool stroll to a 3-0 victory at Manchester United.
All the action from La Liga and Serie A matches played on Monday
A Dani Carvajal strike in the ninth-minute of stoppage time rescued Real Madrid, earning them a 3-2 comeback win at home against bottom side Almeria on Sunday in a frantic LaLiga tussle that was marked by VAR controversy.
Real Madrid tightened their grip on top spot by beating Alaves 3-0 at home in La Liga on Sunday to provisionally move five points ahead of nearest challengers Barcelona despite coach Zinedine Zidane making a string of changes in defence.
Atletico Madrid's Brazil-born forward Diego Costa has signed a formal letter stating his wish to play for adopted country Spain, ending a tug-of-war between the two powerhouses over the in-form 25-year-old.
Casemiro headed an 89th minute winner to earn Real Madrid a barely deserved 2-1 victory at Las Palmas in La Liga on Sunday as they closed the gap on second-placed Atletico Madrid to four points.
Four men were arrested in Madrid, police said, three of whom were members of "a radical group of fans of a Madrid club", who were previously flagged during matches as "high risk" to help curb violence during games.
Dada present at event bringing La Liga to India.
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Villarreal continued their impressive revival after a season in the second division when Jeremy Perbet and Jonathan Pereira struck in a 2-1 win at home to Espanyol in La Liga on Thursday.
The home side spurned two chances to extend their advantage before the break but Barca levelled in the 52nd minute when Luis Suarez glanced in Lionel Messi's free kick.
Villarreal tightened their grip on fourth place in La Liga when Nigerian forward Ikechukwu Uche's last-gasp strike snatched a 1-0 win at fellow promoted side Elche on Monday.
Real Madrid beat Leganes 4-2 on Wednesday despite resting key players including Cristiano Ronaldo and Gareth Bale as goals from Alvaro Morata and James Rodriguez helped them stay top of La Liga after Barcelona cruised to a 3-0 win over Sevilla.
A towering Diego Godin header secured Atletico Madrid a 1-1 draw against Barcelona and a first La Liga title for 18 years in a thrilling climax to the campaign on Saturday.
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Real Madrid had courted Mbappe in the past but failed to land the player, who signed a contract extension with PSG in May 2022 when the Spanish club had a bid rejected.
Girona reclaimed top spot in LaLiga after beating champions Barcelona 4-2
Valencia lost ground in the battle with Atletico Madrid and Sevilla for third place in La Liga when they conceded a late Aritz Aduriz equaliser in a bad-tempered 1-1 draw at Athletic Bilbao on Thursday.
La Liga champions Barcelona's domestic struggles continued as they dropped points for the third game in a row, drawing 1-1 at home to Athletic Bilbao on Saturday after Lionel Messi and Sergio Busquets had begun the match on the substitutes' bench.
Real Madrid's hopes of overhauling La Liga leaders Barcelona suffered a stinging blow when they were held to a 2-2 draw at home to Valencia.
A round-up of Saturday's football action in La Liga, Bundesliga and Ligue 1.
Dani Olmo came off the bench in the second half to give Barcelona the spark they needed on his debut, against Rayo Vallecano.