A method for monitoring a capability of an exhaust-gas analyzer probe in an exhaust passage of an internal combustion engine operated with lean combustion to measure rich gas. Exhaust gas is diffused in the exhaust-gas analyzer probe from the exhaust passage via a diffusion barrier into a measuring cavity of the exhaust-gas analyzer probe, and with the aid of a pump cell having an inner pump electrode and a second pump electrode, by applying a pump voltage between the electrodes, oxygen is pumped into or out of the measuring cavity according to a flowing pump current. During a lean operation mode of the internal combustion engine, the pumping direction of the pump cell is reversed during a diagnostic phase and oxygen is pumped into the measuring cavity, and the capability of the exhaust-gas analyzer probe to measure rich gas is inferred from the pump current and/or the pump voltage.