The effect of the degree of degradation of the components of a model municipal plastic waste (a mixture of low-density polyethylene, high-density polyethylene, polypropylene and high-impact polystyrene) on the toughness and stability of recyclates compatibilised with a cooperative compatibilisation system (a mixture of ethylene–propylene statistical and styrene–butadiene block copolymers with a secondary amine-based stabiliser) was studied. It was shown that good impact strength was achieved for recyclates having components with a low or medium degree of degradation. Mechanical properties of recyclates having the components with a high degree of degradation are deteriorated. The addition of the cooperative compatibilisation system leads to a higher thermo-oxidative stability of recyclates irrespective of the degree of degradation of their components. Photo-oxidative stability of the recyclates is low but it can be improved to a satisfactory level by the addition of carbon black or a commercial photo-stabiliser.