A self-consistent analysis of the JPC=0++ partial waves obtained from high-statistics Kπ, KK̄, and ππ data has been performed to verify the existence and to determine the resonance parameters of the I=12 and I=0 scalar mesons. A mass-dependent parametrization of the Kπ partial wave yields one and only one strange scalar meson, the κ(1510), with a width of several hundred MeV. Isoscalar O++ mesons found in simultaneous fits to KK̄ and ππ data are the ε(800), S*(1005), and ε′(1540) with widths of about 1000, 8, and 200 MeV, respectively. No simple interpretation of all these states and the δ(980) and possible δ′(1300) as qq̄ mesons, qq̄ qq̄ bound states, or gluon-gluon bound states exists. Possible candidates for an SU(3) nonet of qq̄ states are found to be (a) ε(800), ε′(1540), σ(980), and κ(1540) or (b) S*(1005), ε′(1540), σ′(1300), and κ(1540). © 1979 The American Physical Society.