Аннотация:For the Sturm–Liouville equation of standard form on the complex plane, we study the existence of potentials with monodromy-quasifree singular points, i.e., singular points such that some power of the monodromy matrix M is independent of the spectral parameter and equal to ±I, where I is the identity matrix. For the matrix M and its trace, we state necessary and sufficient conditions for the singular point of the potential to be monodromy-quasifree.Examples of potentials with such singular points, including branching points, are given. (ссылка для просмотра полного текста статьи https://rdcu.be/cWCPs)