  Light gravitino productions in association with a neutralino (selectron) in
e^+e^- (e^-\gamma) collisions are restudied in a scenario that the lightest
supersymmetric particle is a gravitino and the produced neutralino (selectron)
promptly decays into a photon (electron) and a gravitino. We explicitly give
the helicity amplitudes for the production processes by using the effective
goldstino interaction Lagrangian, and present the cross sections with different
collision energies and mass spectra. We also examine selection efficiencies by
kinematical cuts and beam polarizations for the signal and background
processes, and show that the energy and angular distributions of the photon
(electron) can explore the mass of the t-channel exchange particle as well as
the mass of the decaying particle at a future e^+e^- (e^-\gamma) collider.
