A method for monitoring a vehicle exhaust system may include (1) measuring exhaust-gas temperature at an outlet side of an exhaust pipe section which is intended to accommodate a component with a purifying activity, (2) measuring exhaust-gas temperature at an inlet side of the exhaust pipe section, and (3) comparing a time curve of the outlet-side temperature with a time curve of the inlet-side temperature, wherein the comparison comprises determining a time derivative of the outlet-side temperature or of the inlet-side temperature. Alternatively, the method may include (1) measuring exhaust-gas temperature at an outlet side of an exhaust pipe section which is intended to accommodate a component with a purifying activity, (2) determining a calculated value for the exhaust-gas temperature at the outlet side based on at least one of the heat-storing and fluid-dynamic action of the component, and (3) comparing a time curve of the measured outlet-side temperature with a time curve of the calculated value.