Nearby starburst galaxies have consistently shown anomalous Lyalpha/Hb
eta ratios. By reanalyzing the published IUE/optical observations, we
show that most starbursts present a normal Lyalpha emission, consisten
t with case B recombination theory, provided extinction laws appropria
te to their metallicities are used. This implies that extinction is mo
re important than multiple resonant scattering effects. The anomalous
emission and absorption lines present in a few remaining galaxies are
simply explained if they are observed in the postburst phase, between
about 10(7) and 10(8) yr after the start of the burst. We use updated
stellar population synthesis models to show that anomalous ratios are
produced by the aging of stellar populations, since the underlying ste
llar Lyalpha line is important in the cooler massive stars. The inferr
ed low duty cycle of massive star formation accounts naturally for the
failure to detect large numbers of Lyalpha-emitting galaxies in deep
surveys and at high redshift. Some testable predictions of the propose
d scenario are also discussed.