Resident of the lower Ormeau Road in Belfast have the RUC's assertion of controversial would be best decided agreement between marchers and local communities.
Six Orange marches through the nationalist area were rerouted or stopped last year and two went through.
A spokesman for the Lower Ormeau Concerned Community group said "The RUC has ample powers under the Public Order order to stop, reroute or alter any parade, legal or otherwise."
He claimed the RUC lacked the "political direction to make a clear decision on all parades and accept the verdict of local communities to reroute those which are unwelcome".
Residents of Garvaghy Road in Portadown, Co Armagh, yesterday met the RUC Chief Constable, Sir Hugh Annesley, to avert trouble during marches through the area this year.
Last July, there was a three day stand off between the RUC and Orangemen at Drumcree, one mile away, when tlie Order tried to parade down the road.