Gaussian sum‐rules, which are related to a two‐parameter Gaussian‐weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum‐rules, including instanton effects, for scalar gluonic and non‐strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum‐rules are remarkably consistent in their prediction of masses of approximately 1 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons. © 2003 American Institute of Physics