The copolymerization and terpolymerization reactions of the vinyl‐substituted phenolic stabilizers, 6‐tert‐butyl‐2‐(1,1‐dimethylhept‐6‐enyl)‐4‐methylphenol, o‐allylphenol, 4‐methylstyrene‐2,6‐di‐tert‐butylphenol and 2,6‐di‐tert‐butyl‐4‐allylphenol, with propene and carbon monoxide, by using the solvent‐stabilized palladium(II) phosphine complex [Pd(dppp)(NCCH3)2](BF4)2 (dppp, 1,3‐bis(diphenylphosphino)propane) as a catalyst precursor and methanol as a co‐catalyst, is described. The influence of functional α‐olefins/CO units, distributed statistically along the propene/carbon monoxide (P/CO) copolymer backbone, on the molecular weight, glass transition temperature (Tg), elastic behavior and stability of the high‐molecular‐weight P/CO copolymer has been investigated. Loss of both elasticity and transparency were observed upon incorporating o‐allylphenol as a termonomer. The terpolymers, which contain phenolic stabilizers, were shown to be more stable when compared to the stabilizer‐free polyketones. In contrast to the propene/carbon monoxide copolymer, no degradation was observed for the 2,6‐di‐tert‐butyl‐4‐allylphenol/P/CO terpolymer; instead, the molar masses increased.