The present invention relates to polypiperidine compounds capable of conferring to polymeric materials, particularly polyolefins, a high stability against photodegradation and oxidative action of air, which belong to the HALS category and have the following general formula (I) in which x can be zero or 1; y is between 1 and 10; m and n, which may be different or equal to each other, range from 2 to 8; A represents a NPiR1 group or a NR2R3 group; and Pi represents the group of formula (II) wherein R1 is selected from the group consisting of H, C1-C4 straight-chain and branched-chain alkyl groups; R2 and R3 can be the same or different and are selected in the group consisting of H, C1-C8 straight-chain and branched-chain alkyl groups, cyclic alkyl groups having from 5 to 12 carbon atoms, or form together with the nitrogen atom a heterocyclic ring having from 5 to 7 members, comprising other heteroatoms such as O, R4 is selected from the group consisting of H, C1-C4 straight-chain and branched-chain alkyl group, and OR5 group, wherein R5 is selected from the group consisting of H, C1-C8 straight-chain or branched-chain alkyl groups. The invention also relates to processes for the preparation of the compounds according to the invention.