  The Dalitz decays eta -> e^+e^-g and omega -> pi^0 e^+e^- have been measured
in the g p -> eta p and g p -> omega p reactions, respectively, with the A2
tagged-photon facility at the Mainz Microtron, MAMI. The value obtained for the
slope parameter of the electromagnetic transition form factor of eta,
Lambda^{-2}_eta=(1.97+/-0.11_tot) GeV^{-2}, is in good agreement with previous
measurements of the eta -> e^+e^-g and eta -> mu^+mu^-g decays. The uncertainty
obtained in the value of Lambda^{-2}_eta is lower than in previous results
based on the eta -> e^+e^-g decay. The value obtained for the omega slope
parameter, Lambda^{-2}_omega_pi^0 = (1.99+/-0.21_tot) GeV^{-2}, is somewhat
lower than previous measurements based on omega -> pi^0 mu^+mu^-, but the
results for the omega transition form factor are in better agreement with
theoretical calculations, compared to earlier experiments.
