The delayed S1 --> S0 fluorescence from the first electronically excited singlet state S1 of an aromatic compound in liquid solution is caused by diffusion-controlled triplet-triplet annihilation (TTA) T1 + T1 --> S1 + S0. For a random spatial distribution of triplet state molecules at time t = 0, Smoluchowski's theory for a diffusion-controlled reaction predicts a time-dependent rate constant k(d)(t) of TTA with k(d)(0) must-greater-than k(d)(infinity). If the triplet state is populated by optical excitation S0 --> S1 and subsequent intersystem crossing S1 --> T1, it is principally impossible to generate a random distribution of triplet state molecules. Since the pair S1 ... T1 is an intermediate during the creation of a triplet pair T1 ... T1, Forster energy transfer S1 + T1 --> S0 + T(n) may compete with the generation of T1 ... T1 at short intermolecular distances. As a consequence, one expects an anti-Smoluchowski behavior of TTA with k(d)(0) much-less-than k(d)(infinity), or with respect to the intensity of the delayed fluorescence, a strong initial rise. The anti-Smoluchowski behavior of a delayed fluorescence has been observed for the first time (with anthracene in a viscous alkane mixture as solvent). The anti-Smoluchowski behavior can be quantitatively described with a simple kinetic model, which contains only four parameters: the diffusion coefficient of molecules in T1, the Forster radius for the S1-T1 energy transfer, and two parameters specifying an exponential distance dependence of the annihilation rate constant for a triplet pair.The delayed S1 --> S0 fluorescence from the first electronically excited singlet state S1 of an aromatic compound in liquid solution is caused by diffusion-controlled triplet-triplet annihilation (TTA) T1 + T1 --> S1 + S0. For a random spatial distribution of triplet state molecules at time t = 0, Smoluchowski's theory for a diffusion-controlled reaction predicts a time-dependent rate constant k(d)(t) of TTA with k(d)(0) must-greater-than k(d)(infinity). If the triplet state is populated by optical excitation S0 --> S1 and subsequent intersystem crossing S1 --> T1, it is principally impossible to generate a random distribution of triplet state molecules. Since the pair S1 ... T1 is an intermediate during the creation of a triplet pair T1 ... T1, Forster energy transfer S1 + T1 --> S0 + T(n) may compete with the generation of T1 ... T1 at short intermolecular distances. As a consequence, one expects an anti-Smoluchowski behavior of TTA with k(d)(0) much-less-than k(d)(infinity), or with respect to the intensity of the delayed fluorescence, a strong initial rise. The anti-Smoluchowski behavior of a delayed fluorescence has been observed for the first time (with anthracene in a viscous alkane mixture as solvent). The anti-Smoluchowski behavior can be quantitatively described with a simple kinetic model, which contains only four parameters: the diffusion coefficient of molecules in T1, the Forster radius for the S1-T1 energy transfer, and two parameters specifying an exponential distance dependence of the annihilation rate constant for a triplet pair.