Police are appealing for two men to come forward after CCTV showed them to be in an area where a man was found with serious head injuries.
A 59-year-old man was found injured in an alleyway in Huddersfield's town centre at 0610 BST.
CCTV in the area shows the man staggering down the alleyway and out of view of the camera at about 0045 BST.
Police are keen to speak to two men seen walking along the alleyway about the same time.
They stop and look in the direction of where the 59-year old had walked but then continue walking.
The injured man is in a critical condition at Huddersfield Royal Infirmary.
Police are keen to speak to the men to see if they can provide any information about how the 59-year-old may have been injured.
They are described as white and in their late teens or early twenties.
One had short brown hair and was wearing a dark waist length top with a white diagonal stripe across it.
The second man also had short dark hair and was wearing black trousers and a blue denim jacket.
Police inquiries are ongoing.