The results of systematic studies on the surface energy γ and its polar γP and dispersion γD components of statistical copolymers of styrene and butadiene, acrylonitrile and butadiene, and butyl acrylate and vinyl acetate, with regard to their thermal prehistory, are generalized. Along with copolymers, the surfaces of their composing homopolymers were examined. We obtained the energy characteristics of the adhesive surfaces of copolymers that contacted with air, high-energy aluminium Al (γ = 160 mJ/m2), and the low-energy substrate surface of polytetrafluoroethylene F4 (PTFE) (γ = 18 mJ/m2). The surfaces of copolymers in contact with air, aluminium, and PTFE were investigated for the first time. It was found that the surface energy of these copolymers tended to occupy an intermediate value between the surface energy of the homopolymers. The additive nature of the change in the surface energy of the copolymers with their composition, as previously established in the works of Wu, extends to the dispersive component of the free surface energy γD and the critical surface energy γcr, according to Zisman. It was shown that a significant influence on the adhesive activity of copolymers was exerted by the substrate surface upon which the adhesive was formed. Thus, for the butadiene-nitrile copolymer (BNC) samples formed in contact with a high-energy substrate, their surface energy growth was associated with a significant increase in the polar component of the surface energy γP from 2 mJ/m2 for the samples formed in contact with air, to an increase from 10 to 11 mJ/m2 for the samples formed in contact with Al. The reason why the interface influenced the change in the energy characteristics of the adhesives was the selective interaction of each macromolecule fragment with the active centres of the substrate surface. As a result, the composition of the boundary layer changed and it became enriched with one of the components. The structure of such layers is nonequilibrium. The thermal annealing of copolymers in the mode of a stepwise temperature increase led to a convergence in the values of γ, asymptotically tending to the value characteristic of the surface of the copolymers formed in air. The activation energies for the processes of the conformational rearrangements of the macromolecules in the surface layers of the copolymers were calculated. It was found that the conformational rearrangements of the macromolecules in the surface layers occurred as a result of the internal rotation of the functional groups that determined the polar component of the surface energy.