Data taken with the Crystal Barrel detector on (p) over bar p --> pi(0)eta and pi(0)eta' are presented at (p) over bar momenta from 600 to 1940 MeV/c. A partial wave analysis finds two alternative solutions, one significantly preferred over the other. Both contain resonances of similar masses and widths, but different coupling constants and phases. The favoured solution contains a J(PC) = 0(++) resonance at 2025 +/- 30 MeV with Gamma = 330 +/- 75 MeV, and three 2(++) resonances as follows: (i) at 1990(-30)(+15) MeV with Gamma = 190 +/- 50 MeV (dominantly P-3(2)), (ii) at 2060 +/- 20 MeV with Gamma = 195 +/- 30 MeV (dominantly F-3(2)), (iii) at 2265 +/- 20 MeV with Gamma = 235(-35)(+60) MeV (dominantly F-3(2)), There are two 4(++) resonances at 2025 +/- 40 MeV with Gamma = 250(-55)(+80) MeV and at 2300 +/- 20 MeV with Gamma = 230 +/- 40 MeV. Errors cover systematic errors and statistical fluctuations of 3 sigma. (C) 1999 Published by Elsevier Science B.V. All rights reserved.