Stellar population synthesis is a tool for modelling galaxies and their spectral energy distributions. By combining the spectra of every star within a galaxy, it becomes possible to form the spectrum of the galaxy as a whole. This requires a large collection of stellar spectra which, ideally, contains spectra for every kind of star in the model galaxy. To contribute to the development of stellar population synthesis and model atmospheres, I examine two such collections of stars, the MARCS and ATLAS9 theoretical stellar libraries. I compare 18 spectra of model stars for which both libraries have performed calculations. Stars with three different temperatures were chosen (8000K, 4500K and 3500K). For each temperature, three values of metallicity and two values of effective gravity were chosen. I find a mismatch in the spectra of the medium and low temperature model stars (4500K and 3500K), in addition, a difference in molecular features (~7000Å) is found in the 3500K low metallicity models ([Me/H]=-2.5). I conclude that this difference is caused by missing molecular opacities for the calcium hydride (CaH) molecule in the ATLAS9 library. Four possible causes of the overall mismatch are discussed: the temperature structure of the models; the geometry of the models; and partition functions used for the calculation of the models. I conclude that none of these four sources could produce the mismatch. This leaves room for further investigation into the cause of the mismatch.