One bomb went off on the Strand Road; the other outside a tourist office.
This is the latest attack on the tourist office by the Real IRA which is hoping to wreck the city of culture celebrations next year.
The bomb attacks could put off visitors from coming to the North West, hitting hopes of a tourism boost spin-off for Co Donegal.
The PSNI have mounted a major security operation in Derry which is expected to last well into Friday.
The PSNI District Commander in Derry, Superintendent Stephen Martin, said the attacks were “cowardly and callous”.
“Thankfully we are not dealing with mass casualties or worse this evening,” he said.
“The reckless acts of those who planted these devices stand in stark contrast to those of the brave officers who entered these areas to evacuate local residents and businesses.
“The people in Derry do not want this disruption.”
The extent of any damage to property is not yet known.
The North’s Justice Minister, David Ford, said those behind the bomb could have killed.
“The rationale for these attacks has to be challenged. Those responsible must know that violence does not bring them any closer to their stated objective,” he said.
Former mayor of Derry Colum Eastwood said: “This is another attack on the people of Derry by people who are enemies of the city and enemies of Ireland.”
The Ulster Unionist leader, Tom Elliott, blamed dissident republicans for the attack.
“This type of fascism was part of our past. It has no place in our future.”