We search for new resonances, Y, with mass M Y , in the range from 30 to 89 GeV, produced via the reaction e + e − → Z 0 → γ Y, where Y subsequently decays into e + e − , μ + μ − or hadrons. We use 5.5.pb −1 of data collected in the energy range 88.2 ⩽ s ⩽ 94.2 GeV, near the Z 0 peak. We obtain the following upper limits, at the 95% confidence level, on the product of the branching ratios: BR(Z 0 → γ Y) × BR(Y → e + e − ) < 2.8 × 10 −4 for 30 < M Y < 89, BR(Z 0 → γ Y × BR(Y → μ + μ − ) < 2.3 × 10 −4 for 30 < M Y < 89, BR(Z 0 → γ Y) × BR(Y → hadrons) < 4.7 × 10 −4 for 30 < M Y < 86. These limits are valid for resonances with widths smaller than our mass resolution.