Abstract: Searches for CP violation in the two-body decays Ds+→h+π0 and Ds+→h+η (where h+ denotes a π+ or K+ meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb−1 or 6 fb−1 of integrated luminosity. The π0 and η mesons are reconstructed using the e+e−γ final state, which can proceed as three-body decays π0→ e+e−γ and η → e+e−γ, or via the two-body decays π0→ γγ and η → γγ followed by a photon conversion. The measurements are made relative to the control modes Ds+→KS0h+ to cancel the production and detection asymmetries. The CP asymmetries are measured to beACPD+→π+π0=−1.3±0.9±0.6%, ACPD+→K+π0=−3.2±4.7±2.1%, ACPD+→π+η=−0.2±0.8±0.4%, ACPD+→K+η=−6±10±4%, ACPDs+→K+π0=−0.8±3.9±1.2%, ACPDs+→π+η=0.8±0.7±0.5%, ACPDs+→K+η=0.9±3.7±1.1%, where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of ACP in these decay modes to date.