Abstract The resonant substructure of D 0 → π+π−π+π− decays is studied using data collected by the CLEO-c detector. An amplitude analysis is performed in order to disentangle the various intermediate state contributions. To limit the model complexity a data driven regularization procedure is applied. The prominent contributions are the decay modes D 0 → a 1(1260)+ π−, D 0 → σ f 0(1370) and D 0 → ρ(770)0 ρ(770)0. The broad resonances a 1(1260)+, π(1300)+ and a 1(1640)+ are studied in detail, including quasi-modelindependent parametrizations of their lineshapes. The mass and width of the a 1(1260)+ meson are determined to be m a1(1260)+ = 1225 ± 9 (stat) ± 17 (syst) ± 10 (model) MeV/c 2 and Γa1(1260)+ = 430 ± 24 (stat) ± 25 (syst) ± 18 (model) MeV. The amplitude model of D 0 → K + K −π+π− decays obtained from CLEO II.V, CLEO III, and CLEO-c data is revisited with improved lineshape parametrizations. The largest components are the decay modes D 0 → ϕ(1020)ρ(770)0, D 0 → K 1(1270)+ K − and D 0 → K(1400)+ K −. The fractional CP -even content of the decay D 0 → π+π−π+π− is calculated from the amplitude model to be F + 4π  = 72.9 ± 0.9(stat) ± 1.5(syst) ± 1.0(model) %, consistent with that obtained from a previous model-independent measurement. For D 0 → K + K −π+π− decays, the CP -even fraction is measured for the first time and found to be F + KKππ  = 75.3 ± 1.8 (stat) ± 3.3 (syst) ± 3.5 (model) %. The global decay rate asymmetries between D 0 and D ¯ 0 $$ {\overline{D}}^0 $$ decays are measured to be A C P 4 π = + 0.54 ± 1.04 stat ± 0.51 syst % $$ {\mathcal{A}}_{CP}^{4\uppi}=\left+0.54\pm 1.04\ \left(\mathrm{stat}\right)\pm 0.51\ \left(\mathrm{syst}\right)\right\% $$ and A C P KKππ = + 1.84 ± 1.74 stat ± 0.30 syst % $$ {\mathcal{A}}_{CP}^{KK\pi \pi}=\left+1.84\pm 1.74\ \left(\mathrm{stat}\right)\pm 0.30\ \left(\mathrm{syst}\right)\right\% $$ . A search for CP asymmetries in the amplitude components yields no evidence for CP violation in either decay mode.