[en] The Mark III detector at SPEAR was used to observe the exclusive radiative decay psi → γ eta π⁺π^-. The eta c was seen as an intermediate state in this decay, psi → γ eta c, eta c → eta π⁺π^-. The product branching ratio B(psi → γ eta c) B(eta c → eta π⁺π^-) was measured to be 4.2 +- 0.5 (stat) +- 0.5 (sys) x 10^-4. Other resonant structure was observed in the eta π⁺π^- spectrum in the range 1 < M/sub eta π⁺π-/ < 2 GeV/c², which appears to decay via X → delta^+-π^-+, delta^+- → eta π^+-. A spin-parity analysis was performed to determine the quantum numbers of the resonances responsible for this structure. However, the result was seen to be model dependent, so that it was not possible to conclusively resolve the underlying structure in the spectrum. No evidence was seen for the decay iota → eta π⁺π^-. An upper limit was set for the ratio of branching ratios for iota → eta ππ relative to iota → KKπ, R = B(psi → γiota)B(iota → eta ππ)/B(psi → γiota)B(iota → KKπ) < 0.2 (90% C.L.). 54 references, 59 figures