The incident happened overnight between Friday and Saturday, from a farm a short distance away from the Orrock Quarry Road, near Auchtertool.
The vehicles are described as a Green John Deer tractor with the registration plate SP08 DFA and a blue Valtra tractor with the registration plate SP16 BFU.
Police believe the vehicles have travelled on to the Orrock Quarry Road, and are looking to hear from any person who have seen tractors travelling on this road late Friday night in to the early hours of Saturday morning.
Officers are continuing with inquiries and ask anyone with information that can help trace the vehicles and those responsible to come forward.
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Those with information are asked to contact Police Scotland via 101, quoting incident number 1064 of February 23. Alternatively a report can be made to Crimestoppers anonymously on 0800 555 111.
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