A commercial premises in Yelland was broken into between 6pm, on Tuesday 23 March, and 8am, on Wednesday 24 March, and cash was taken.
In a second break-in, a domestic garage was targeted between 4.15am and 4.49am on Wednesday 24 March but nothing appears to have been taken.
While two crimes have been reported, investigating officers believe there may have been other break-ins and are appealing for any other possible victims to come forward.
Officers request that residents and businesses in the area check their storage areas and report any loss of items to police.
Police would also like to hear from anyone who may have witnessed any suspicious activity or may have CCTV footage in the area.
Anyone with any information is asked to contact police on 101 or via email at [email protected] quoting crime reference, CR/022903/21 for Yelland or CR/022863/21 for Instow.