In the last decade, a rather new phenomenon related to subsynchronous oscillations (SSO) in a wide frequency range has emerged in modern power grids with power converters. The consequences of these oscillations can be severe system accidents, which have already occurred in various power systems. Taking into account the importance of studying such oscillations for effective mitigation and the existing gaps in understanding the mechanisms of SSO occurrence due to different combinations of used controllers in the inverter control system, as well as the grid parameters, a frequency analysis of simplified grid inverter models is performed. As a result, five different mechanisms of SSO occurrence, the affecting factors and the level of inverter model detail required for the adequate study of SSO are justified. The developed detailed state–space model allowed for verifying the obtained results, as well as identifying an additional sixth mechanism of SSO occurrence. The common condition for the occurrence of all the identified SSO mechanisms is a weak grid with a short-circuit ratio of less than two. The results of control hardware-in-the-loop testing confirmed the conclusions drawn. As a result, a classification of SSO occurrence mechanisms was formed, reflecting their causes and distinctive features.