This article examines the structure of co-authorship networks’ stability in time. The goal of the article is to analyse differences in the stability and size of groups of researchers that co-author with each other (core research groups) formed in disciplines from the natural and technical sciences on one hand and the social sciences and humanities on the other. The cores were obtained by a pre-specified blockmodeling procedure assuming a multi-core–semi-periphery–periphery structure. The stability of the obtained cores was measured with the Modified Adjusted Rand Index. The assumed structure was confirmed in all analysed disciplines. The average size of the cores obtained is higher in the second time period and the average core size is greater in the natural and technical sciences than in the social sciences and humanities. There are no differences in average core stability between the natural and technical sciences and the social sciences and humanities. However, if the stability of cores is defined by the splitting of cores and not also by the percentage of researchers who left the cores, the average stability of the cores is higher in disciplines from the scientific fields of Engineering sciences and technologies and Medical sciences than in disciplines of the Humanities, if controlling for the networks’ and disciplines’ characteristics. The analysis was performed on disciplinary co-authorship networks of Slovenian researchers in two time periods (1991–2000 and 2001–2010).