The first incident happened between 8.30pm and 8.45pm on Sunday evening at Suffolk Rise, Sheepridge.
A man was walking along the road when he saw three men behind him, two of whom were carrying knives.
He was then surrounded and one of the group held a knife to his face and demanded property.
Another member of the group then searched him as the third person stood around holding a knife.
As this took place the victim noticed a fourth member of the group, who appeared to be acting as a look out.
The four men then made off. Nothing was stolen during the incident but police said the victim was left in shock.
Officers want to speak to four males in connection with the incident.
They were described as aged in their teens, around 5ft10 tall and black. They were all wearing black jackets with the hoods up and their faces were covered.
The second incident happened less than an hour later, between 9.20pm and 9.30pm, as a 55-year-old woman was walking along Belle Vue Crescent.
As she walked towards the junction of Well Grove three men approached her.
The first threatened her with a knife and demanded money while two other stood behind her to prevent her from fleeing.
The victim gave the suspects the change she had, before one tried to snatch her handbag.
She struggled and all three left the scene, walking up Belle Vue Crescent towards Brackenhall Road.
Officers want to speak three men in connection with this incident.
They were described as black, in their late teens and all wearing dark clothing, wearing black ski masks, and described as being of medium build and around 5ft4 tall.
Police Constable Jack Hodges of Huddersfield CID said: “These are two serious offences and given the proximity and the times of these two incidents we believe that they are linked.
“Thankfully neither victim was injured clearly this was a frightening experience for the two people involved and they were both understandably left shaken.
“I would appeal to anyone who was in or around the area on Sunday evening who may have seen or heard anything suspicious, or who may have seen people matching the suspects in the area to come forward.
“Anyone who has any information about the incident can contact police via 101 quoting crime reference 13160639196 (first incident) or 13160639804 (second incident) or Crimestoppers anonymously on 0800 555 111.”