A Catholic primary school and an Orange hall were attacked by arsonists on Sunday.
A classroom at St Mary's Boys Primary School, Strabane, was destroyed by a fire which was discovered at 4 p.m. on Sunday.
The RUC said it was treating the fire as malicious. A school spokesman said it was obvious the fire had been started deliberately.
"The fire was started in three areas of the room and those responsible were intent on causing as much damage as possible.
"A computer in the classroom was destroyed while everything else, including furniture and books, will have to be replaced," he said. The RUC said the attack was not believed to have been sectarian.
Police said a fire at Wattlebridge outside Newtown butler, Co Fermanagh, was started deliberately. The Orange hall was extensively damaged in the fire, which took several hours to bring under control. Mr George Johnston, the Orange district grand master, said that community relations were very good in the area of the lodge, which draws members from both sides of the Border. He said he was "very disappointed to see the like of this strife being stirred up".
The fire was the second in an Orange hall in Fermanagh in the past two weeks and is believed to be sectarian. There has been a pattern of arson attacks recently on both Orange halls and Catholic schools around the North.
Meanwhile, an SDLP Assembly member has told how her property had been attacked for the sixth time this year. Ms Carmel Hanna said her car was damaged outside her south Belfast home on Saturday night. She believed the attack was sectarian.
"It's not just about the attack on my car. It's about ongoing attacks in the area on innocent people," said Ms Hanna.
She said there was a longstanding problem of loyalist graffiti and displayed a flyer threatening to "remove all republicans from the area".