A method for checking the authenticity of value documents which are transported for their authenticity check past a sensor, and which have a security feature which, as a reaction to a luminescence excitation by an excitation source, both emits a first luminescence at a first wavelength which has as a function of time t a first intensity course y1(t) with a first characteristic time constant τ1 and emits a second luminescence at a second wavelength different from the first wavelength which has as a function of time t a second intensity course y2(t) with a second characteristic time constant τ2, having the following steps: - detecting the first intensity course y1(t) and the second intensity course y2(t) as a function of time t at the same detection location of the security feature using the sensor, - computing a first parameter S1=S(y1(t i)), with i=1,2,...,n, using a scale-invariant function S: R n→ R from a plurality of first intensity values y1(t i) of the first luminescence which are detected at different time points t i during a rise and/or during a decay of the first intensity course y1(t), wherein the computing is carried out with the help of an evaluation device, - computing a second parameter S2=S(y2(t 1))) with i=1,2,...,n, using a scale-invariant function S: R n→ R from a plurality of second intensity values y2(t i) of the second luminescence which are detected at the time points t i during a rise and/or during a decay of the second intensity course y2(t i), wherein within the context of the scale-invariant function S there is formed the quotient P J /P K of two linear functionals P J and P K which respectively map the first intensity values y1(t i) or second intensity values y2(t i) detected at the different time points t i to the space of real numbers, wherein the linear functional P J (y1(t i)) maps the first intensity values y1(t j) detected at one or a plurality of time points t j to the space of real numbers, and that the linear functional P K ((y1(t i) maps the first intensity values y1(t k) detected at a plurality of time points t k to the space of real numbers, and that the linear functional P J (y2(t i)) maps the second intensity values y2(t j) detected at one or a plurality of time points t j to the space of real numbers, and that the linear functional P K ((y2(t i)) maps the second intensity values y2(t k) detected at one or a plurality of time points t k to the space of real numbers, wherein the time point/points t k are different from the time point/points t j, wherein the computing is carried out with the help of an evaluation device, - determining a ratio V between the first parameter S1 and the second parameter S2, wherein the determining is carried out with the help of an evaluation device, - checking the authenticity of the value document using the ratio V or using a value W derived from the ratio V, wherein the ratio V or the value W derived from the ratio V are compared with a reference value or with one or more thresholds, wherein the computing is carried out with the help of an evaluation device. - detecting the first intensity course y1(t) and the second intensity course y2(t) as a function of time t at the same detection location of the security feature using the sensor, - computing a first parameter S1=S(y1(t i)), with i=1,2,...,n, using a scale-invariant function S: R n→ R from a plurality of first intensity values y1(t i) of the first luminescence which are detected at different time points t i during a rise and/or during a decay of the first intensity course y1(t), wherein the computing is carried out with the help of an evaluation device, - computing a second parameter S2=S(y2(t 1))) with i=1,2,...,n, using a scale-invariant function S: R n→ R from a plurality of second intensity values y2(t i) of the second luminescence which are detected at the time points t i during a rise and/or during a decay of the second intensity course y2(t i), - determining a ratio V between the first parameter S1 and the second parameter S2, wherein the determining is carried out with the help of an evaluation device, - checking the authenticity of the value document using the ratio V or using a value W derived from the ratio V, wherein the ratio V or the value W derived from the ratio V are compared with a reference value or with one or more thresholds, wherein the computing is carried out with the help of an evaluation device.