I don't know if they share anything but plesiomorphies with Didelphidae.    From Wordnik.com.  [More on phorusrhacids: the biggest, the fastest, the mostest out-of-placest] Reference

As for whether peradectines are really opossums (as in, true members of Didelphidae), you are right that this classification is probably based on plesiomorphies.    From Wordnik.com.  [More on phorusrhacids: the biggest, the fastest, the mostest out-of-placest] Reference

Note: possum, opossum, any of a family (Didelphidae) of American marsupials that usually have a pointed snout and prehensile tail; especially: a common omnivorous largely nocturnal and arboreal mammal (Didelphis virginiana) of North America having grayish to blackish fur with white on the cheeks.    From Wordnik.com.  [Albert Collins Lyrics] Reference

Visits Caluromys lanatus (Didelphidae) flowers Pseudobombax tomentosum (Bombacaceae). probable case pollination marsupials in Brazil.    From Wordnik.com.  [MyLinkVault Newest Links] Reference

Marsupial (Didelphidae) 71.    From Wordnik.com.  [Journals of Two Expeditions of Discovery in North-West and Western Australia, Volume 2] Reference

Family Didelphidae.    From Wordnik.com.  [Journals of Two Expeditions of Discovery in North-West and Western Australia, Volume 2] Reference