There were demonstrations in Belfast, Ballymoney, Kilrea, Coleraine, Portadown, Downpatrick and Lisburn but the situation was constantly changing, Britain's Press Association reported.
Police said the protests were peaceful, but there were fears of a repeat of the nightly violence throughout the province over the past week, in which the security forces were fired on, cars hijacked and set alight and property attacked.
The Royal Ulster Constabulary released figures on the violence since July 1, saying there had been 280 attacks on the security forces, including 13 shooting incidents. A total of 57 RUC officers and five soldiers had been injured.
There had been 288 petrol bombing incidents, some involving dozens of devices, and police had recovered 941 petrol bombs. Police made 146 arrests and laid charges in 72 cases.
The British government's Northern Ireland secretary, Peter Mandelson, and David Trimble, head of the province's power-sharing executive have both appealed for calm and said dialogue was the only answer to the Drumcree dispute.
Mandelson said the British government would not bow to pressure.
The protests were called by Orange Order officials after Orangemen were prevented on Sunday from conducting a parade down the predominantly Catholic Garvaghy Road in Portadown.
The Orangemen, named for King William III of Orange, were founded in 1795 to protect Protestant interests and have been marching at Drumcree annually since the early 19th century.
They celebrate annually the defeat by William of the Catholic King James II at the Battle of the Boyne on July 12, 1690.
