The invention relates to a method and to an apparatus for recognizing tumorous living cell tissue. It furthermore relates to a method and to an apparatus for recognizing tumorous cell tissue at collected living cell tissue samples. In the method, electromagnetic radiation is emitted with local definition onto cell tissue by a radiation source and, after deactivation of the radiation source, the decay behavior of the inherent fluorescence intensity of the cell tissue excited by the electromagnetic radiation is detected at the cell tissue in a time resolved and spectrally resolved manner at known sampling rate(s) for at least one wavelength using a detector. The difference autocorrelation function C(t) of the intensity decay behavior is determined using the determined measured intensity values, the fractal dimension DF for the respective irradiated cell tissue is calculated from this and the value of the fractal dimension DF is used for a classification with respect to a presence of a tumor in the respective irradiated cell tissue.