The invention relates to a diagnostic method for checking the functionality of a component for the exhaust-gas aftertreatment of an internal combustion engine. For this purpose, in an internal combustion engine, a secondary air supply is provided by means of which an excess of oxygen can be generated in the exhaust gas channel essentially independently of the operating conditions of the internal combustion engine, and wherein said excess of oxygen is utilized for the measurement of an oxygen storage capacity of the component or of a signal change at the component. It is provided that the component is subsequently subjected to a substoichiometric exhaust gas in order that the oxygen release capacity or the signal change upon a change from superstoichiometric exhaust gas to a substoichiometric exhaust gas is also taken into consideration in the diagnosis. The invention also relates to a device for exhaust-gas aftertreatment, which is designed to be able to carry out a method of said type.