For governance decision support in the area of political stability, it is proposed to use cognitive maps and the original technology of the socio-political situation analysis and monitoring based on them. Cognitive maps are considered as a means (1) of an integral representation of a complex multifactorial socio-political situation using various sources of the data; (2) of identification of key factors for situation monitoring in the information space; (3) of development of goals and directions for ensuring political stability, taking into account the interests of interacting stakeholders in the situation. As part of the technology development, an approach is proposed to the organization of monitoring on the weak signals of changes in observed factors of the situation in social media.