The first, a white Ford Transit was located on Dryden Way in Southey Green had having been stolen from the Crookes area of Sheffield.
Officers say the only reason they checked this vehicle was that they drive in the area on a regular basis and hadn't seen it before.
The second, a stolen moped located on Lytton Drive in Parson Cross was returned to its Stannington owner before they had even noticed it was missing.
The officers warned those that stole the vehicles that they would be looking for them and that forensic opportunities were being explored regarding both thefts.
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Anyone with any information about either crime should call police on 101, quoting incident number 873 of 16072018.