Police are reporting that a number of gravestones have been damaged at Dukinfield Cemetery and Crematorium.
The attacks happened overnight between 23 and 24 June.
A spokesperson for Greater Manchester Police's Tameside North and East team said on Facebook: "This is a despicable crime that will cause much distress to families of the loved ones laid to rest at the cemetery.
"We are seeking any information, dash cam footage, mobile phone footage etc that may assist in our investigation.
"We intend to identify those responsible and bring them to justice.
"If you do have any information, please ring 101 quoting CRI/06GG/0014875/22."
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