A method combining the statistical equilibrium theory and the thermodynamics of irreversible processes is used to study the relaxation behaviour in the spin-1 Ising model Hamiltonian with bilinear and biquadratic interactions near the second-order phase transition point or the critical point. In order to study these phenomena in a connected way the assumption is made that the dipole moment (magnetization) and the quadrupole moment order parameters can be treated as fluxes and forces in the sense of Onsager's theory of irreversible thermodynamics. The kinetic equations are characterized by two relaxation times which describe the irreversible process in the cooperative system. It is found that one of the relaxation times approaches infinity near the critical temperature on either side of the transition temperature, whereas the other relaxation time makes a cusp at the critical temperature. Further, the kinetic equations are solved by using the Runge-Kutta method in order to study the relaxation of order parameters. The results are compared with the conventional kinetic theory in the random phase or generalized molecular field approximation and path probability method and a very good overall agreement is found.