A method for detecting accretion or abrasion on a first measuring tube of a flow measuring device. A first temperature as a function of time is registered via a first temperature sensor, which is arranged on the first measuring tube in such a manner that, between the first temperature sensor and the medium, at least one measuring tube wall of the first measuring tube is embodied. Parallel in time, a second reference temperature as a function of time is registered by a second temperature sensor, which is spaced from the first temperature sensor and thermally coupled to the medium. Therefrom, at least one variable characteristic is determined, and accretion or abrasion on the first measuring tube is detected, if the at least one determined characteristic variable or a variable derived therefrom deviates by more than a limit value from a predetermined reference variable.