It is known that irreversibilities of hysteresis nature of global or local scale, lead to the necessity to revise the methods of solving the main problems of hydrodynamic modelling and analysis of dynamic systems, as they can radically affect the traditional conclusions and practical recommendations. It is assumed that in the steady-state mode of motion or filtration, phase displacements make all sorts of oscillations in the vicinity of the unstable position, due primarily to irreversible hysteresis phenomena and jumps arising from the instability of the front of oil displacement by water, the manifestation of capillary effects, hysteresis of phase transitions, irreversibility of deformations under excessive load at large pressure drops, including hydraulic fracturing. With this purpose in the theory of catastrophes the dynamic models of growth are investigated and control parameters are selected with the calculation and the possibility to predict the expected local irreversibilities and instabilities before the onset of bifurcation. Hysteresis behaviour in the filtration process is generated by lithological differences of geofluidodynamic medium and its geological and physical characteristics and properties of saturating fluids. And as a rule, it is provoked by not always adequate, excessive external load on the tested medium. The proposed solutions are part of a new concept of unsteady waterflooding, which provides for early prediction and taking measures in case of instability of the displacement front and, as a consequence, water breakthrough into production wells. It is of great interest to prevent the consequences of these negative effects on the quantitative components of technological and economic indicators, in the case of oil field development we are talking about the final recovery factor of oil, gas and condensate. System optimisation of oil field development is designed for a certain technological and economic effect, including additional oil production, effective mobilisation and saving of injected and withdrawn water and gas.