In the first incident, the body of 52-year-old T P Anirudhan, who was posted in the Third Battalion, was found with a bullet wound in his right temple this morning, they added.
His service pistol, a motorcycle and a helmet were found near his body, police said.
They said that his belongings were found intact, indicating that he was not attacked.
It was suspected that he shot himself yesterday. He had come to office of the Delhi Police Security Wing in Chanakyapuri, police said.
His family members could not explain why he took such extreme step. No suicide note was found, they said.
In the second incident, 54-year-old Hanuman Samay, who was posted in the Police Control Room unit, died after shooting himself in the head inside a PCR van today, police said.
He was under depression and was undergoing treatment for the last four-five years at the Ram Manohar Lohia Hospital, they said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)