  We utilize nonlinear pulsation models to reproduce the observed light and
color curves for two samples of bump Cepheid variables, 19 from the Large
Magellanic Cloud and 9 from the Small Magellanic Cloud. This analysis
determines the fundamental parameters mass, luminosity, effective temperature,
metallicity, distance and reddening for the sample of stars. The use of light
curve shape alone to determine metallicity is a new modelling technique
introduced here.
  The metallicity, distance and reddening distributions for the two samples are
in agreement with those of similar stellar populations in the literature. The
distance modulus of the Large Magellanic Cloud is determined to be
18.54$\pm$0.018 and the distance modulus of the Small Magellanic Cloud is
determined to be 18.93$\pm$0.024. The mean Cepheid metallicities are $Z =
0.0091\pm0.0007$ and $0.0050\pm0.0005$ for the LMC and SMC, respectively.
  The masses derived from pulsation analysis are significantly less than those
predicted by stellar evolutionary models with no or mild convective core
overshoot. We show that this discrepancy can not be accounted for by
uncertainties in our input opacities or in mass-loss physics. We interpret the
observed mass discrepancy in terms of enhanced internal mixing in the vicinity
of the convective core during the main-sequence lifetime and find that the
overshoot parameter $\Lambda_{c}$ rises from 0.688$\pm$0.009H_p at the mean LMC
metallicity to 0.746$\pm$0.009H_p in the SMC.
