From the point of view of the intrinsic rotation, the Jupiter Trojans are not as well characterized as the main belt asteroids, primarily because the available sample of lightcurves is small and mainly restricted to the largest objects. We have obtained rotational periods and lightcurve amplitudes for 6 Trojan asteroids, which range between values of 5.7 and 9.6 h and 0.08 and 0.59 magnitudes, respectively. This sample includes an object of absolute visual magnitude H=11.5 m, which corresponds to physical radii ranging from 35 to 22 km, assuming albedos between 4% and 10%. The values of the rotation periods found are consistent with those found for the Main Belt Asteroids in the same size range.