This contribution discusses the sensibility of the transient response of a fluid in a pipeline with respect to the existence of two leaks which occur simultaneously assuming that only pressure and flow rate are measured at the extremes of the line. It is shown that the four unknown parameters of the fluid model produced by two simultaneous leaks are identifiable considering the transient response of the fluid. The analysis is made generating a family of nonlinear lumped parameters models of the fluid with only two unknown parameters and introducing the parameter z/sub eq/ which parameterizes the subset of two indistinguishable leaks with steady state data. The evaluation of the quadratic integral error of the output vector by simulation for any two members of the family with parameter z/sub eq/ shows the possibility to identify the unknown parameters of two leaks considering the transient behavior at the extremes of the pipeline. Thus, the identification of the parameters can be achieved off-line using the family of models with data of the transient response; diverse optimization algorithms can be implemented for this purpose. To estimate the parameters of a water pilot pipeline with leaks, here an extended Kalman filter of reduced order has been implemented in a recursive structure. The advantages of the novel family of models and its specifications for the leak location problem are shown with an example.