A passenger said to be in his 50s was stabbed to death in board a train from Guilford to London.
The victim was stabbed by a man whose identity is currently unknown and on the run with a knife.
Witnesses say the murder happened after the two men began fighting. Both men exchanged punches before the man with the knife stabbed the other and he died at the scene despite desperate attempts by paramedics to save him.
The attacker is thought to have got off the train just one stop into the journey and fled into the surrounding Clandon area.
No arrests have been made yet but police are now in the area, attempting to identify and trace the man responsible for the murder.
Detective Superintendent Gary Richardson from British Transport Police, said:
This was a shocking and violent attack which took place on-board a train in broad daylight.
Officers from BTP are with the family and have deployed a specially trained family liaison officer to support them through this difficult time.
We know that this was an incredibly frightening incident for passengers travelling on the train.
We believe that the suspect and victim boarded the train at London Road at 1.01pm and we would encourage who was on this train to come forward regardless of whether or not they think they can help our investigation.
We believe the suspect departed the train at Clandon station.
Passengers and members of the public can expect to see an increased presence by BTP and Surrey Police officers at Horsley and Clandon as our enquiries continue.
We would advise anyone in the local area who sees anyone they think maybe the suspect to contact 999 immediately.