The events with two photons and missing (transverse) energy collected by the DELPHI detector at centre-of-mass energies between 130 GeV and 183 GeV have been studied to search for processes of the type e(+)e(-) --> YY with the subsequent decay Y --> X gamma, where X is an undetectable neutral particle. Reactions of this kind are expected in supersymmetric models, where the Y particle can be either the lightest neutralino, decaying to a photon and a gravitino, or the next-to-lightest neutralino, decaying to a photon and the lightest neutralino. To study the case of long-lived Y particles, a search for single-photon events with the reconstructed photon axis pointing far from the beam interaction region has also been performed. No evidence for a deviation from Standard Model expectations has been observed in the data and upper limits have been derived on the signal cross-section as a function of the the X and Y masses and of the Y mean decay path.