According to Christian news agency World Watch Monitor they happened in Dutse, the capital of the northern state of Jigawa, earlier this month.
World Watch Monitor says bulldozers escorted by police and the area's Executive Secretary of Urban Development, Alhaji Garba Isa, knocked down the Redeem Christian Church of God and the Lord Chosen Church.
It also says police refused to let church members go in to collect valuables from the church and chased away people trying to video the demolitions.
Alhaji Garba Isa said authorities knocked down the churches because they'd been built illegally, failing to acquire the correct papers from government. He also said notices had been sent to both churches urging them to apply for the permission papers on three separate occasions.
But Rev Yakubu Musa, chairman of the Christian Association of Nigeria for Jigawa, said the pastors of both churches applied for the permission papers but were refused.
Both churches had been standing for several years before authorities demolished them: the Lord Chosen Church had been operating for 17 years and the Redeem Christian Church of God was operating for eight years.
Rev Musa told the Monitor: "It was a terrible experience, with so many Christians who witnessed the demolition crying.
"I felt so bitter because we were in a situation where you have been cheated and you cannot talk.
"They only concentrated on the church buildings because we are not many and we don't have anyone in the government to speak for us."
Jigawa adopted Islamic Sharia law in the 2000s.
Six more churches in the state are due to be demolished.
