[en] The extended Peierls-Hubbard model is used to study the competition of the spin-density-wave (SDW) and charge-density-wave (CDW) states as well as the attendant localized excitations in quasi-one-dimensional systems like MX-chains. The ground state properties are first studied as a function of the Coulomb interaction U and the on-site electron-phonon coupling λ₂. The SDW state dominates in the region of large U and small λ₂, while the CDW state prevails in the opposite limit. In the intermediate region these two states compete with each other, one being stable, whereas the other being metastable. The localized excitations (polarons and excitons) are studied in detail in each region using the Bogoliubov-de Gennes formalism. The self-trapped excitons (STE) in the CDW dominating regime contain locally non-vanishing SDW distortions and vice versa. As λ₂ increases, the number of bound states changes from two to four for the exciton case and from two to three for the polaron case. Upon its further increase, one type of STE with a certain pattern of SDW distortion and charge transfer is transforming into another type of STE with a different pattern. The possibilities of verifying the ground state properties in optical and transport experiments and identifying these local excitations in Raman and ENDOR measurements are discussed. (author). 25 refs, 11 figs