We search for new resonances, Y, with mass MY, in the range from 30 to 89 GeV, produced via the reaction e+e− → Z0 →γY, 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 Z0 peak. We obtain the following upper limits, at the 95% confidence level, on the product of the branching ratios: BR(Z0 → γY) × BR(Y → e+e−) < 2.8 × 10−4 for 30 < MY < 89, BR(Z0 →γY × BR(Y → μ+μ−) < 2.3 × 10−4 for 30 < MY < 89, BR(Z0→ γY) × BR(Y → hadrons) < 4.7 × 10−4 for 30 < MY < 86. These limits are valid for resonances with widths smaller than our mass resolution.