Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Polyhazard models constitute a flexible family for fitting lifetime data. The main advantages over single hazard models include the ability to represent hazard rate functions with unusual shapes and the ease of including covariates. The primary goal of this paper was to include dependence among the latent causes of failure by modeling dependence using copula functions. The choice of the copula function as well as the latent hazard functions results in a flexible class of survival functions that is able to represent hazard rate functions with unusual shapes, such as bathtub or multimodal curves, while also modeling local effects associated with competing risks. The model is applied to two sets of simulated data as well as to data representing the unemployment duration of a sample of socially insured German workers. Model identification and estimation are also discussed.273357376Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)