[en] A theory is developed to model the excitations in a dimerized, spin-1/2 system with a magnetically ordered ground state and where the dimer exchange constant is antiferromagnetic. This method starts by considering the energy levels of a single dimer in the effective, staggered magnetic field due to the mean-field ordering of the surrounding dimers. Pseudo-boson operators are introduced which create and annihilate these excitations, and the Hamiltonian of the magnetic system can be rewritten in terms of these operators and then diagonalized to yield one doubly degenerate transverse mode and a longitudinal singlet mode for each non-equivalent dimer in the magnetic unit cell. The dimer theory has been used to model the measured dispersion relations in the anti ferromagnetically ordered phase of the alternating-chain compound CuWO₄. It provides a good fit to the data and is as successful as spin-wave theory in accounting for the transverse excitations although with different values of the exchange constants. In addition the transition temperature and the size of the reduced moment at T 0 K calculated in the dimer theory are closer to the experimental values of CuWO₄ than those calculated by spin-wave theory. An important difference between these two models lies in their predictions of the longitudinal excitations: whereas in spin-wave theory these are regarded as two-magnon events resulting in a continuum of scattering, in the dimer theory one well defined mode is expected. An experimental measurement of the longitudinal excitations should distinguish between these models. (author)