We investigate the influence of dynamic surface tension on the stability of trapped or attached microbubbles. Two kinds of equilibrium radii are observed for shrinking microbubbles. The first one is related to the equilibrium surface concentration of surfactant. The other is related to the decrease of the surface tension due to the compression of the surface area at the maximum surfactant concentration. The experimental results are compared with the numerical solutions by taking the influence of the dynamic surface tension on the gas diffusion into account. The simulations agree well with the experimental results.