A device exploded outside a property on Ervey Road, which belongs to a Catholic police officer in the early hours of Wednesday morning.
It caused damage to the front door of the house, but no one was inside at the time.
In a second attack, a bomb has been found in the garden of the home of a doctor who treats prisoners in police custody on Learmount Road.
The GP, who works as a forensic medical officer at local police stations, is the chairman of the Foyle Hospice.
Three men - two aged 36 and one aged 28 - have been arrested in the Derry area in connection with the attacks.
There are also unconfirmed reports that there may be other devices in the area, with police appealing for the public to be vigilant.
Chief Superintendent Stephen Martin said he had no doubt the Real IRA were behind the attacks.
"This police officer is a member of the community, he spends his life serving the community," he said.
"As to why they targeted the doctor... I don't think I could begin to try and understand how a man who has been a General Practitioner - a man who has given 40 years service to the community - is deemed to be a target."
Supt Martin said that throughout the Troubles doctors were regarded "as neutral and independent."
This just is indicative of the recklessness and the desperation of these small anti-peace groups when they can find some rationale to target a doctor.
Chief Superintendent Stephen Martin
Bishop of Derry, Dr Seamus Hegarty, described the attacks as cowardly and branded those responsible as "criminals".
"These senseless acts offer nothing but pain and misery to both the intended victims and the wider community," he said.
"In condemning the attack on the police officer I take the opportunity to acknowledge the courage of the many young people who have joined the PSNI and hope that despite the threat to their lives, family and homes they will continue in the very noble vocation of serving the community in PSNI.
"I ask those who would consider engaging in such cowardly activities to instead join with the many people who are working to make our community and the island of Ireland a better place for all people", the statement ended.
Thomas Conway, SDLP Claudy councillor and Foyle District Policing Partnership Chairman said: "Up until now the dissidents have only targeted within the confines of Derry City and this is the first instance where they have moved to rural areas."
"Whilst an attack on anyone's home is despicable, rural areas and homes are much more isolated and are softer targets.
"It's also worrying as those responsible have obviously acquired a degree of intelligence about the homes and movements of their targets.
He added: "These were deplorable actions. There is a real sense of anger in this community.
"I condemn these without question and urge anybody with information to pass it to the PSNI."
Policing Board chair Brian Rea said the attacks are "totally unjustifiable".
"It is fortunate that no-one was killed or seriously injured.
"The people who carried out these mindless acts of violence have nothing positive to contribute to our society and will not succeed in destroying the huge progress that has been made in policing across communities," he said.
Meanwhile, a 36-year-old woman was arrested in Derry on Wednesday afternoon on suspicion of dissident republican activity.
She was detained by detectives from the PSNI's Serious Crime Branch and is helping police with their enquiries.