The anomalous fluorescence of azulene-emission from S-2 rather than S-1-was first recognized by Beer and Longuet-Higgins 40 years ago. Femtosecond laser studies and spectroscopic line width measurements have now established that radiationless decay from S-1 to the ground state takes place in less than 1 ps. In this paper we show how such ultrafast S-1 decay can be explained by relaxation through an unavoided S-1/S-0 crossing (i.e., a conical intersection). The S-1 relaxation dynamics of azulene from its Franck-Condon structure are modeled semiclassically using a hybrid quantum-mechanical/force-field potential (MMVB) which reproduces the structure of the ab initio CASSCF potential energy surface. This simulation suggests that the S-1 --> S-0 decay takes place in femtoseconds before a single oscillation through the crossing is completed.