  We report a study of the processes e+e- -> eta gamma and e+e- -> etaprime
gamma at a center-of-mass energy of 10.58 GeV, using a 232 fb^-1 data sample
collected with the BABAR detector at the PEP-II collider at SLAC. We observe
20+6-5 eta gamma and 50+8-7 etaprime gamma events over small backgrounds, and
measure the cross sections sigma(e+e- -> eta gamma)
=4.5+1.2-1.1(stat)+-0.3(sys) fb and sigma(e+e- -> etaprime
gamma)=5.4+-0.8(stat)+-0.3(sys) fb. The corresponding transition form factors
at q^2 = 112 GeV^2 are q^2|F_eta(q^2)|=0.229+-0.030+-0.008 GeV, and
q^2|F_etaprime(q^2)|=0.251+-0.019+-0.008 GeV, respectively.
