A search for the CP-violating strong decays eta -> pi(+)pi(-) and eta ' (958) -> pi(+)pi(-) has been performed using approximately 2.5 x 10(7) events of each of the decays D+ -> pi(+)pi(+)pi(-) and D-s(+) -> pi(+)pi(+)pi(-), recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb(-1) of pp collision data recorded during LHC Run 1 and 0.3fb(-1) recorded in Run 2. No evidence is seen for D-(s)(+) -> pi(+)eta((')) with eta((')) -> pi(+)pi(-), and upper limits at 90% confidence level are set on the branching fractions, B(eta -> pi(+)pi(-)) < 1.6 x 10(-5) and B(eta' -> pi(+)pi(-)) < 1.8 x 10(-5). The limit for the eta decay is comparable with the existing one, while that for the eta' is a factor of three smaller than the previous limit. (C) 2016 The Author. Published by Elsevier B.V.