Modern experiments and quantum calculations have revealed interesting trends in core electron spectra of oligomers and polymers. In particular, the core electron chemical shifts show salient features that are structurally dependent, but which have not been completely understood. From pi-electron theory we derive a model for core electron binding energy shifts in conjugated molecules and polymers. The alternant behavior of the site dependent shifts in the linear and polycyclic hydrocarbons are predicted by the model. The alternations show end-to-bulk amplification, respectively, damping for the cyclic and the linear polyenes. The polycyclic hydrocarbons show the strongest alternation effects for the bulk atoms, while for the polyenes the alternation is strongest for the terminal atoms. The analysis is based on renormalized perturbation theory and on the analytic solutions of the Huckel equations. The theory and the proposed model can be applied also for investigations of the influence of impurities on physical properties of polymers.