Elastomers which have excellent stability to prevent oxidative, thermal, dynamic, light-induced and/or ozone-induced degradation comprise, as stabilizers, at least one compound of the formula I[R—S(═O)m—CH2—CH(OH)—CH2]n—N(R1)2-n—R2, (I)in whichR is C4–C20alkyl, hydroxyl-substituted C4–C20alkyl; phenyl, benzyl, α-methylbenzyl, α,α-dimethylbenzyl, cyclohexyl or —(CH2)qCOOR3, and, if m is 0, R may additionally be