The Rapid Eye Mount (REM) fast-slewing robotic telescope has been conceived to immediately point and observe optical counterparts of γ-Ray Bursts detected by satellites. It started operations at the European Southern Observatory (La Silla, Chile) in June 2003. V(RI)c observations of the open clusters Trumpler 26 and Trumpler 31 were carried out during the telescope commissioning time. Membership to the clusters was photometrically investigated and MS stars about 1.5 magnitudes fainter than those revealed in any previous study were detected. The present data can constitute a starting point for a detailed investigation of late-type stars and stellar activity in such clusters.