The boys, aged 15 and 16, were stabbed in Ilminster Avenue, in Knowle West, at about 11.20pm on Saturday, Avon and Somerset Police said.
The attack was carried out by a group of people who fled the scene in a car.
Police have launched a murder inquiry and are actively hunting more suspects as well as witnesses who were on a bus at the time of the killings.
A 44-year-old man and a 15-year-old boy have been arrested and are in custody. A vehicle has also been seized.
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The victims sustained stab wounds and were taken to two hospitals – Southmead Hospital and Bristol Royal Hospital for Children – by ambulance, where they died in the early hours of Sunday morning.
Police said the boy’s families were with them at hospital and the Major Crime Investigation Team is keeping them informed of developments.
Neither boy has yet been identified and post-mortem examinations will be carried out in due course.
Detectives are keen to speak to passengers on a bus which was on Ilminster Avenue at the time of the attack.
Bristol Commander Superintendent Mark Runacres said: “There are further suspects that are being sought amongst the group we believe are responsible.”
He said: “At about 11.20pm last night we received a report two people stabbed in an attack carried out by a group of people on Ilminster Avenue. The first officer was on the scene within minutes to provide first aid before the boys were taken to hospital by ambulance. Tragically neither survived their injuries.”
A word from Bristol Commander Supt Mark Runacres at the cordon in Ilminster Avenue, Bristol. pic.twitter.com/oyV7qVRtmE
— Avon and Somerset Police (@ASPolice) January 28, 2024
He said police were keen to speak to anybody on the double-decker last night.
“This is an incredibly shocking and tragic incident where two young boys, who had their whole lives ahead of them, have sadly died.
“Our collective thoughts are with their families at what is undoubtedly a very difficult time. Specialist family liaison officers will now be assigned to the families to provide them with support and keep them updated on the investigation.
“There are a significant number of properties within the cordon and we would like to apologise for the disruption caused, but we hope people understand the importance of the work being carried out.”
Supt Runacres said house-to-house inquiries were under way and several witnesses had been identified.
He also confirmed CCTV and doorbell footage was being gathered and a mobile police station was being set up near the scene.
A spokesman for Ilminster Avenue Academy on the same road the boys were killed, said that a psychiatrist would be on site for pupils on Monday.
The school posted: “We are deeply saddened to hear about the events that took place on Ilminster Avenue last night.
“We will be holding assemblies tomorrow morning and will make sure that children are given the opportunity to talk about what happened.”
Anyone with information about the incident or with any relevant footage, has been asked to contact 101 and quote reference 5224023382.