  We have analyzed the influence of the stellar populations, from which SN
progenitors come from, on the observational outcome, including the metal free
Pop. III. We use our models to study the evolution of the progenitor, the
subsequent explosion and the light curves.
  For Type Ia, the variation of the main sequence mass of the progenitor of the
exploding WD, produces an offset in the maximum-decline relation of 0.2 mag.
This effect is critical for the use of high redshift Type Ia SNe as
cosmological standard candles. In contrast, the metallicity does not change the
above relation (at maximum, Delta M_V < 0.06 mag).
  For Type II, we find a dependence of the light curve properties with both,
main sequence mass and metallicity of the progenitor, and we identify a rather
homogeneous subclass, {\it Extreme} II-P, that may be used as a quasi-standard
candle. Note that, although not as good as Type Ia for distance determinations,
Type II are expected to occur since the first stars were formed.
