After hearing more than two years of evidence, the jury also concluded that the behaviour of Liverpool supporters on the day did not cause or contribute to Britain's worst sports stadium tragedy.
The jury also found that there were errors in police planning for the match and on the day of the match which caused or contributed to the dangerous situation.
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Relatives of the victims have fought a long campaign to get to the heart of what happened during the disaster.
Some emerged from the courtroom hugging and in tears.
The jury has been sitting since March 2014 in a purpose-built courtroom in Warrington, northwest England, 15 miles (25 kilometres) outside Liverpool.
The disaster occurred on April 15, 1989 during an FA Cup semi-final between Liverpool and Nottingham Forest at Sheffield Wednesday's Hillsborough stadium in northern England.
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Seeking to alleviate a crush that had developed outside the ground at the Leppings Lane End shortly before kick-off, the police match commander opened an exit gate.
It enabled 2,000 fans to stream into the ground and they piled into the already over-full pens behind the goal at that end of the ground, causing a fatal crush.Hillsborough disaster verdict is 'long overdue justice', says PM Cameron
British Prime Minister David Cameron hailed the verdict as "long overdue justice" for the victims.
Landmark day as the #Hillsborough inquest provides long overdue justice for the 96 Liverpool fans who died in the disaster.
— David Cameron (@David_Cameron) April 26, 2016
I would like to pay tribute to the extraordinary courage of #Hillsborough campaigners in their long search for the truth.
— David Cameron (@David_Cameron) April 26, 2016
Here's a short clip of the tragedy with interviews from the survivors:
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