Comment: JEL: G22The subject of the present article is the study of correlations between large insurance companies and their contribution to systemic risk in the insurance sector. Our main goal is to analyze the conditional structure of the correlation on the European insurance market and to compare systemic risk in different regimes of this market. These regimes are identified by monitoring the weekly rates of returns of eight of the largest insurers (five from Europe and the biggest insurers from the USA, Canada and China) during the period January 2005 to December 2018. To this aim we use statistical clustering methods for time units (weeks) to which we assigned the conditional variances obtained from the estimated copula-DCC-GARCH model. The advantage of such an approach is that there is no need to assume a priori a number of market regimes, since this number has been identified by means of clustering quality validation. In each of the identified market regimes we determined the commonly now used CoVaR systemic risk measure. From the performed analysis we conclude that all the considered insurance companies are positively correlated and this correlation is stronger in times of turbulences on global markets which shows an increased exposure of the European insurance sector to systemic risk during crisis. Moreover, in times of turbulences on global markets the value level of the CoVaR systemic risk index is much higher than in "normal conditions".