One of the classical approaches to solving color reproduction problems, such as color adaptation or color space transform, is the use of a low-parameter spectral model. The strength of this approach is the ability to choose a set of properties that the model should have, be it a complete coverage of a color triangle or an accurate description of the addition or multiplication of spectra, knowing only the tristimulus corresponding to them. The disadvantage is that some of the properties of the mentioned spectral models are confirmed only experimentally. This work is devoted to the theoretical substantiation of various properties of spectral models. In particular, we prove that the banded model is the only model that simultaneously possesses the properties of closure under addition and multiplication. We also show that the Gaussian model is the limiting case of the von Mises model and prove that the von Mises model unambiguously covers the color triangle in cases of both convex and non-convex spectral loci.