The first crash took place on the B4393 between Llanfyllin and Llanfechain at around 9.45am on July 20. One person was injured in the car accident and was taken to hospital via ambulance to the Royal Shrewsbury Hospital.
The second traffic collision occurred at 11.30am when a car was in collision with a lorry in Llanfyllin. Fire crews had to be called to the scene to rescue two people from the car. The injured people were also taken to the Royal Shrewsbury hospital for treatment.
A spokeswoman for Dyfed-Powys Police said, "Police attended the first scene just outside Llanfechain and aided in the recovery of the vehicle."
Witnesses to both accidents are being asked to come forward and help Dyfed-Powys Police with their enquiries.
It has not yet been reported if any car crash claims have been made for either of the accidents.
*Where replacement vehicle costs can be recovered from the insurance company of the person who caused the accident.
Where this person is untraceable or uninsured, or where there is a dispute over liability, a replacement vehicle cannot
be provided.