Barcelona start the defence of their La Liga title on Sunday at Athletic Bilbao, the team who thrashed them 5-1 on aggregate in the Spanish Super Cup.
Luis Enrique's squad appears weaker than last season's Treble-winning selection, with Pedro and Xavi leaving.
Summer signings Arda Turan and Aleix Vidal cannot play until January because of a transfer ban.
Real Madrid begin their season under new boss Rafael Benitez with a match away to newly promoted Sporting Gijon.
They sacked Carlo Ancelotti after finishing two points behind Barca and exiting in the Champions League semi-final.
Benitez's major outfield signings have been right-back Danilo from Porto and midfielder Mateo Kovacic from Inter Milan.
The goalkeeping situation at Real has dominated the summer at the Bernabeu following the tearful departure of Iker Casillas after 25 years at the club.
Manchester United goalkeeper David De Gea has been strongly linked with a move to Real, but that deal has yet to materialise.
Keylor Navas is favourite to start against Sporting but Kiko Casilla, a summer signing from Espanyol, is also in contention.
"Losing Xavi and Pedro hasn't made us weaker. Teams like Barca lose very good players and get back very good players," said Barca defender Marc Bartra.
"We still have a good group of homegrown players, with those who have joined us from other clubs, we'll continue to be unstoppable."
Former Everton and Manchester United manager David Moyes guided Real Sociedad to 12th place having taken over as coach of the Basque side in November 2014.
But the 52-year-old Scot has been keen to play down the growing expectations in San Sebastian ahead of their opener against Deportivo La Coruna.
"I don't think that right now we have to have Europe as a goal. Considering what we did last season, looking to Europe is a very big step," Moyes said.