This paper considers the composite "core-shell" fibers ageing. A physical model of ageing is proposed. The stress state due to the structural relaxation processes in the shell results from the ageing. The ageing model was verified experimentally. The agreement between the model and experiment is found. A weak periodical boundary layer between the core and the shell is formed as a result of the composite fiber ageing process. The values characterizing the boundary layer (thickness and shear modulus) were obtained.