The invariant mass spectrum of the eta 'pi(+)pi(-) final state produced in two-photon collisions is obtained using a 673 fb(-1) data sample collected in the vicinity of the Gamma(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We observe a clear signal of the eta(c)(1S) and measure its mass and width to be Md(eta(c)(1S)) = (2982.7 +/- 1.8(stat) +/- 2.2(syst) +/- 0.3(model)) MeV/c(2) and Gamma(eta(c)(1S)) = (37.8(-5.3)(+5.8)(stat) +/- 2.8(syst) +/- 1.4(model)) MeV/c(2). The third error is an uncertainty due to possible interference between the eta(c)(1S) and a nonresonant component. We also report the first evidence for eta(1760) decay to eta'pi(+)pi(-); we find two solutions for its parameters, depending on the inclusion or not of the X(1835), whose existence is of marginal significance in our data. From a fit to the mass spectrum using coherent X(1835) and eta(1760) resonant amplitudes, we set a 90% confidence level upper limit on the product Gamma B-gamma gamma(eta'pi(+)pi(-)) for the X(1835).