We present the results of an amplitude analysis of the spin parity components as a function of mass of the (K{sup +}{bar K}{sup 0}{pi}{sup {minus}}) system as produced in the reaction {bar p}p {yields} (K{sup +}{bar K}{sup 0}{pi}{sup {minus}}) X. Two peaks are observed in the (K{sup {minus}}{bar K}{sup 0}{pi}{sup {minus}}) spectrum, one at (1279 {plus minus} 2) MeV/c{sup 2} with a width of (21 {plus minus} 2) MeV/c{sup 2}, and one at (1417 {plus minus} 3) MeV/c{sup 2} with a width of (62 {plus minus} 5) MeV/c{sup 2}. The amplitude analysis was performed in sixteen 20 MeV/c{sup 2} mass intervals from 1.24 to 1.56 GeV/c{sup 2}. The waves used for the fitting were J{sup PG} = 0{sup {minus}+}, 1{sup ++}, 1{sup +{minus}}, and background. 12 refs., 8 figs