  The OGLE data base is used in conjunction with Kurucz atmosphere models to
generate sets of period, effective temperature and luminosity for fundamental
and overtone Magellanic Cloud Cepheids. The Florida pulsation code (with linear
turbulent convection) is then used to compute masses for these stars, assuming
an average composition of ($X$=0.716, $Z$=0.010) for the LMC and of ($X$=0.726,
$Z$=0.004) for the SMC. The average $M$--$L$ relation for the fundamental
Cepheids matches closely that for the first overtone Cepheids for each
Magellanic Cloud. Neither the SMC nor the LMC average $\Log M$--$\Log L$
relations are straight, but have a noticeable curvature.
  In view of the uncertainties in distance and reddening we have adopted three
different choices for these quantities. The results based on the 'long'
distance scale to the clouds give a better agreement between theory and and
observations than the 'short' one.
  All the current evolutionary tracks predict systematically larger masses for
given luminosities than our observationally derived ones, especially at the
high end. Moreover, our study confirms that the evolutionary tracks of the low
mass stars in SMC are not in agreement with the observations as they do not
extend sufficiently blueward and do not penetrate deep enough into the
instability strip, or not at all.
  The inference of masses directly from the observational database yields a
novel and strong constraint on evolutionary calculations.
