Searches for CP violation in the decays D(s)+ -> ηπ+ and D(s)+ -> η'π+ are performed using pp collision data corresponding to 6 fb(-1) of integrated luminosity collected by the LHCb experiment. The calibration channels D(s)+ -> ηπ+ and D(s)+ -> ϕπ+ are used to remove production and detection asymmetries. The resulting CP-violating asymmetries are

A(CP) (D+ -> ηπ+) = (0.34 ± 0.66 ± 0.16 ± 0.05)%,

A(CP) (D(s)+ -> ηπ+) = (0.32 ± 0.51 ± 0.12)%,

A(CP) (D+ -> η'π+) = (0.49 ± 0.18 ± 0.06 ± 0.05)%,

A(CP) (D(s)+ -> η'π+) = (0.01 ± 0.12 ± 0.08)%,

where the first uncertainty is statistical, the second is systematic and the third, relevant for the D+ channels, is due to the uncertainty on A(CP) (D+ -> ϕπ+). These measurements, currently the most precise for three of the four channels considered, are consistent with the absence of CP violation. A combination of these results with previous LHCb measurements is presented.