In this work we perform a detailed experimental and theoretical analysis of the properties of amplified spontaneous emission (ASE) in a rhodamine-6G-doped graded-index polymer optical fiber when the fiber is pumped either longitudinally or transversally with respect to the fiber axis. The dependence of the ASE threshold and efficiency on fiber length has been compared for both schemes of excitation. A theoretical model for longitudinal excitation has been carried out by means of the laser rate equations as functions of time, distance traveled by light and wavelength. The analysis takes into account that the fiber is a typical graded-index POF in which the radial distributions of light power density and dye concentration are not uniform. The theoretical calculations agree satisfactorily with the experimental results. The photodegradation of the ASE intensity has also been measured for both pumping schemes.