The 60-year-old actress, who played Princess Leia Organa in Star Wars saga, is in the ICU of a Los Angeles hospital.
Carrie Fisher had heart problems during a flight from London to LA, and passengers attempted to revive her with CPR.
Her mother, actress Debbie Reynolds, said on Twitter: “Carrie is in stable condition. If there is a change, we will share it. For all her fans & friends. I thank you for your prayers & good wishes.”
Carrie Fisher had been on tour promoting her latest book, The Princess Diarist.
According to TMZ, the cardiac arrest happened about 15 minutes before the plane landed in LA. A doctor who was travelling on the plane administered CPR.
Paramedics then spent a further 15 minutes administering more CPR to Carrie Fisher before getting a pulse, TMZ reported.
Carrie Fisher appeared in the original Star Wars trilogy and Star Wars: The Force Awakens, a sequel released in 2015.
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