Abstract: Amplitude models are constructed to describe the resonance structure of D-0 -> K-pi(+) pi(+) pi(-) and D-0 -> K+ pi(-)pi(-)pi(+) decays using pp collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of 3.0 f b(-1). The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes D-0 -> a(1)(1260)(+) K- and D-0 -> K-1(1270/1400)(+)pi(-) being prominent in D-0 -> K-pi(+) pi(+) pi(-) and D-0 -> K+pi(-)pi(-)pi(+), respectively. Precise measurements of the lineshape parameters and couplings of the a(1)(1260)(+), K-1(1270)(-) and K(1460)(-) resonances are made, and a quasi model-independent study of the K(1460)(-) resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be R-K3 pi = 0.459 +/- 0.010 (stat) +/- 0.012 (syst) +/- 0.020 (model), which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle gamma and studies of charm mixing and CP violation.