Both took place overnight on Wednesday into Thursday, and in the first incident, damage was caused in overcoming the security of a house on the Bankend Road.
In the second, damage was caused to an exhibition building at Caerlaverock castle.
Nothing was taken in either of these break-ins.
PC Lawrence Nelson at Dumfries said: “While nothing appears to have been stolen, the security of the building was breached on both occasions.
“We need the public to work with us to help put a stop to these crimes.”
PC Nelson added: “In particular we are interested in identifying the occupants of a white coloured Ford Transit type van which was seen in the Glencaple area in Wednesday 1 June 2016.
“Anyone who may have any information which might help is asked to call Police Scotland at Dumfries on 101.”
Break-ins spark police probe
BREAK-INS to properties in Glencaple and Caerlaverock are being probed by police.
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