The main aim of this paper is the development of a structural theory for models of complete Horn theories with non-maximal spectra. A termal lemma, proved in the paper, permits to prove the existence of a prime model over any independent set of models of a complete Horn theory with non-maximal spectrum. It is proved that any model may be decomposed into submodels of smaller depths. This gives the possibility to characterize models of Horn theories with non-maximal spectra. Lower and upper bounds of the spectra of complete Horn theories are found. This gives a proximate characterization of the spectrum of a complete Horn theory if its depth is 1 or \(>\omega\).