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The paper deals with the methods of statistical analysis of dependent competing risks in the presence of covariates. The problem of identification of marginal and joint distributions of competing random variables is recalled and certain identifiability results in the framework of regression models are presented. The main objective is then to study the case when the correlation of competing variables depends on covariates, as this phenomenon has not been taken into account in the most of papers dealing with the identifiability of competing risks models with regression. Such a dependence is demonstrated and estimated on a real example with unemployment data.