We report the first evidence for the eta(b)(2S) using the h(b)(2P) -> eta(b)(2S)gamma transition and the first observation of the h(b)(1P) -> eta(b)(1S)gamma and h(b)(2P) -> eta(b)(1S)gamma transitions. The mass and width of the eta(b)(1S) and eta(b)(2S) are measured to be m(eta b(1S)) = (9402.4 +/- 1.5 +/- 1.8) MeV/c(2), m eta(b(2S)) = (9999.0 +/- 3.5 +/- 2.8 -1.9) MeV/c(2), and Gamma(eta b)(1S) = (10.8(-3.7-2.0)(+4.0+4.5)) MeV. We also update the h(b)(1P) and h(b)(2P) mass measurements. We use a 133.4 fb(-1) data sample collected at energies near the d5S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.