  By using a one-zone chemical and spectrophotometric evolution model of a disk
galaxy undergoing a dusty starburst, we investigate, numerically, the optical
spectroscopic properties in order to explore galaxy evolution in distant
clusters. We adopt an assumption that the degree of dust extinction
(represented by $A_V$) depends on the ages of starburst populations in such a
way that younger stars have larger $A_V$ (originally referred to as selective
dust extinction by Poggianti & Wu 2000). In particular, we investigate how the
time evolution of the equivalent widths of [OII]$\lambda$3727 and H$\delta$ is
controlled by the adopted age dependence. This leads to three main results: (1)
If a young stellar population (with the age of $\sim$ $10^6$ yr) is more
heavily obscured by dust than an old one ($>$ $10^8$ yr), the galaxy can show
an ``e(a)'' spectrum characterized by strong H$\delta$ absorption and
relatively modest [OII] emission. (2) A dusty starburst galaxy with an e(a)
spectrum can evolve into a poststarburst galaxy with an a+k (or k+a) spectrum
0.2 Gyr after the starburst and then into a passive one with a k-type spectrum
1 Gyr after the starburst. This result clearly demonstrates an evolutionary
link between galaxies with different spectral classes (i.e., e(b), e(a), a+k,
k+a, and k). (3) A dusty starburst galaxy can show an a+k or k+a spectrum even
in the dusty starburst phase if the age-dependence of dust extinction is rather
weak, i.e., if young starburst populations with different ages ($\le$ $10^7$
yr) are uniformly obscured by dust.
