The Hamiltonian and equation of motion for the order parameter of a single-mode standing-wave laser system with saturable absorber are given in detail. Three stationary solutions of the equation are obtained near the threshold; their stability is analysed. The results show that the stationary behavior (nonequilibrium phase transition, bistability, critical exponents) of standing wave system near the threshold is similar to the of a traveling wave system qualitatively, but they differ quantitatively. Among she diffefences, it is worth to emphasize that it is possible to realize I-(one of the three stationary solutions) branch experimentally, what is not possible in tho travoling-waye case.