The instability of two fluid nonequilibrium flow model is examined. Over the published works the all source or sink and exchange terms on the right side of partial differential equation system have been taken into account. The system /with continuity, energy, state, momentum, heat transfer equations/ has been linearized and the space-time double Laplace transformation has been used. The eigenvalues of complex transfer matrix have been calculated. For a nuclear reactor /at the blowdown period/ the instabilities have been examined in the function of different physical parameters. The positions of roots in the s time plane in the function of wavelength indicate the local instability of aperiodic type often with oscillation.