Up to now, prominence detection has mainly been considered a binary matter, a syllable or a word being considered as prosodically prominent or not. This contribution aims at developing an automatic detection procedure of gradual prominence. Based on 4 prosodic parameters (relative duration, relative f0, f0 movement and pause duration), the system provides each syllable with a gradual score of prominence ranging from 0 (non-prominent syllable) to 4 (extra-prominent syllable). The automatic detection (ProsoProm) relies on a manually annotated corpus (18 minutes, or 3669 syllables, of speech annotated by three experts) and is cumulative (the relative weight of each parameter is taken into account in order to compute a global score for each syllable). The discussion of the results includes a qualitative analysis of misses and false detections. The agreement between automatic and (median) human annotation reaches a Kappa score of 0.8.