Up to 5,000 people took part in the annual Bloody Sunday march, walking from the Creggan area to the Bogside to commemorate thirteen men shot dead by British paratroopers in 1972.
The PSNI has launched a murder inquiry into the shootings, but relatives complain they don't know how much progress the inquiry has made.
Kate Nash, whose brother William was shot dead, told UTV: "We're looking for accountability for murders and 41 years we still haven't had the full truth.
"We don't even know if the police inquiry has actually started or not. But this is an ongoing struggle and myself and a number of relatives will meet the Deputy Chief Constable shortly to discuss the investigation."
The march was supported by a number of republican groups, including the 32 County Sovereignty Movement and the Republican Network for Unity.
Across the city, meanwhile, loyalists held a parade at the same time.
Organisers billed it as a march for loyalist civil rights and up to 1,000 walked through the city's Waterside carrying banners and union flags.
William Frazer of the Ulster People's Forum was among those on the parade.
He said the protest sent a message to Stormont that the rights of unionists and loyalists were being eroded, adding: "We have no rights.
"The people across Northern Ireland are sick to the back teeth with what's going on. We now want justice, freedom and respect and we want our culture to be left alone."
Police kept a low profile at both events.