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Real said in a statement this afternoon that Di Stefano passed away at 5.15pm local time.
Widely considered one of the greatest ever footballers, Di Stefano scored 216 league goals in 282 appearances for Los Blancos.
He also scored in five successive European Cup finals when Real dominated the continent in the mid-to-late 1950s.
At international level, he represented three countries - Argentina, Colombia and Spain - netting 29 goals in 41 internationals, but never appearing at a World Cup.