Abstract: The robust stability of the all-coefficient adaptive control method with respect to unmodeled dynamics, parameter slowly-varying, non-linearity and bounded disturbance is studied. It is proved that in the presence of unmodeled dynamics and bounded disturbances, the golden section adaptive controller still can stabilize a nominal plant when a gradient update law modified by parameter projection is used to estimate the nominal plant. For systems with multiplicative uncertainty, sufficient conditions are presented for linear slowly varying plants and nonlinear slowly-varying plants with fading memory, respectively.