a propylene polymer composition stabilized against oxidative degradation comprising 100 parts by weight of a propylene polymer , 0 . 001 to 5 parts by weight of a poly composed substantially of monomeric units represented by the following formula ## str1 ## wherein r 1 represents a hydrogen atom or a tertiary butyl group , and 0 . 001 to 5 parts by weight of a dialkylthiodipropionate represented by the following formula s -- c . sub . 2 h . sub . 4 coor ). sub . 2 wherein r represents an alkyl group containing 10 to 20 carbon atoms .