Four other children, including a baby, were taken to hospital.
It was later confirmed that the two eldest boys, aged 14 and 13, had died.
The other children, aged 11, 10, three and seven months, were in hospital last night, but were said to be "conscious" and their injuries are said to be not life-threatening.
The cause of death of the two boys has not yet been established. The children cannot be identified for legal reasons.
A "major incident" was declared after emergency services, including an air ambulance which landed at a nearby school, were called at 7.30am.
Neighbours watched horrified as the children were taken away from the home.
Two adults were led handcuffed from the house in the Shiregreen area of Sheffield.
A friend, who did not want to be named, said the children's mother had said the previous day that it would be a "long night" as the children were ill.
The friend said: "She said the kids weren't well and they could not keep off the toilet. The mum's lovely and raised money for charities."
The children's aunt said: "I don't know what happened."
Superintendent Paul McCurry of South Yorkshire Police said the surviving children were being given then "necessary care they need."
There was no "wider risk to the community" and, he said, a postmortem was taking place.
Neighbour Aaron Brunskill, 29, said "about 20 police cars and four ambulances" were at the house.
He said: "They were taking children away. I have not seen the amount of police like it before."
The school, which cannot be named, confirmed two pupils had "died in tragic circumstances this morning."
Gill Furniss, Sheffield Labour MP, said: "I am deeply saddened by the tragic incident today in my constituency."
Sophie Corcoran is a reporter for Hull Live and the Hull Daily Mail. Her interests include positive news, news about homelessness, court news and breaking news.
You can also call her on 01482 315174 or email email@example.com
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