We define a new class of models for multivariate survival data, in continuous time, based on a number of cumulative hazard functions, along the lines of our family of models for correlated survival data in discrete time [Gross and Huber-Carol (2000, 2002)]. This family is an alternative to frailty and copula models. We establish some properties of our family and compare it to Clayton's and Marshall-Olkin's and derive nonparametric partial likelihood estimates of the hazards involved in its definition.