Abstract: Transdermal absorption morphinan narcotic analgesic or antagonist pharmaceutical polymer matrix dosage units have been developed which comprise a backing layer and an adjoining layer of a solid polymer matrix in which minimum effective doses of morphinan narcotic analgesic or antagonist pharmaceuticals are microdispersed and transdermally supplied. A presently preferred analgesic is hydromoprhone. The dosage units use a biologically acceptable adhesive polymer means to adhere the dosage units to the subject to be treated. The polymer matrix has dispersed one or more skin permeation enhancers. The invention also provides a process for transdermal absorption of said pharmaceuticals in at least minimum dosage amounts.