A search is reported for decays of the Z0 into π0γ, ηγ and η′ (958)γ in e+e− collisions using data collected during a scan around the Z0 mass. In order to search for π0γ final states, in which the two photons from the π0 decay are unresolved, the production of pairs of high-energy electromagnetic clusters is studied. The data are compared with the expectations from the pure QED process e+e− → γγ, and a 95% confidence level upper limit on the branching ratio of the Z0 into π0γ of 4.9 × 10−4 is derived. For η′γ, the decay modes of the mesons that contain two charged particles are largely free from QED background. These modes are used to place upper limits of 4.6 × 10−4 and 2.2 × 10−4 on the corresponding branching ratios of the Z0.