We have studied the luminosity timescales relation of 29 gamma -ray-loud bl
azars with observed minimum variation timescales. Following the acceleratio
n model of Ghisellini and Maraschi (1989 Astrophys. J. 340 189), a relation
between the variation of the timescale in gamma -rays and that in other wa
vebands has been derived. Both the observed and Doppler-corrected gamma -ra
y luminosity timescales relations have been calculated. The observed lumino
sity of the majority of sources is above the Eddington limit. The intrinsic
luminosity of all sources is below the Eddington limit, suggesting that th
e gamma -ray emission of the gamma -ray-loud blazar originates from relativ
istic jets.