Abstract: The inverse parameter problem of the permeable law of the naturally fractured reservoirs with double perosity is of great importance in the exploitation of oil The coefficients in the fluid motion equations are unknown geological parameters. In this paper, the history of matching problem of reservoir systems with double porosity has been discussed from the point of view of the parameter identification of distributed parameter systems, and the problems of identifiability and observability for this system are also dealt with. We have obtained the formulas of Fréchet derivative of the index functional in the identification parameters. These formulas are necessary for calculating identification parameters by a gradient or conjugate gradient method. The conditions of identifiability and observability for the reservoir system with double porosity are given.