  In supersymmetric extensions of the Standard Model with a very light
gravitino, the effective theory at the weak scale should contain not only the
goldstino G, but also its supersymmetric partners, the sgoldstinos. In the
simplest case, the goldstino is a gauge-singlet and its superpartners are two
neutral spin-0 particles, S and P. We study possible signals of massive
sgoldstinos at e+e- colliders, focusing on those that are most relevant at LEP
energies. We show that the LEP constraints on e+e- => photon+S (photon+P), Z+S
(Z+P) or e+e-S (e+e-P), followed by S (P) decaying into two gluon jets, can
lead to stringent combined bounds on the gravitino and sgoldstino masses.
