The first happened in Thornton-Le-Moor, Northallerton, when a woman and her four-year-old son were walking their dog, accompanied by a friend.
A black Alsatian-type dog, which was off its lead, approached them. It attacked the woman’s dog, causing puncture wounds to its leg.
When the woman tried to separate them, the Alsatian-type dog also bit her hand, causing cuts.
The male owner of the Alsatian-type dog then came over, removed his dog and walked away. He is described as being in his 40s with dark, greying hair and wore a leather jacket.
Witnesses to the incident on Wednesday 22 June at around 3.30pm are asked to contact 101, select option 2 and ask to speak to PC Adam Gatenby. Please quote reference number 12160113227.
Police also want to hear from anyone recognising the description of the dog or owner.
Meanwhile, officers in Hull are investigating after a four-year-old boy was bitten by a dog in the park on the Quadrant on Saturday 25 June at 4.30pm.
He was not seriously injured but the police would like to identify the woman in these pictures to speak to her about the incident.
Anyone who can identify the woman from these images is asked to contact Humberside Police on the non-emergency number 101 quoting Ref 2196707.
The attacks, which were made public today, were within days of another at the Handmade Parade in Hebden Bridge.