The formation and evolution of the ``E+A'' (also named ``k+a'' and ``a+k'' types by Dressler et al. 1999) galaxies found in significant numbers in the cores of intermediate redshift clusters has been extensively discussed by many authors. In this paper, we model the spectral, dynamical and morphological evolution of a prime candidate for producing this spectral signature: a dusty starburst associated with a major galaxy merger. We show that as this system evolves dynamically, its spectral type changes from and ``e(a)'' type (exhibiting strong H$��$ absorption and modest [OII] emission -- the identifying features of local dusty starburst galaxies) to a k+a type and then finally to a passive ``k'' type. This result shows that galaxies with an e(a) spectral type can be precursors to the k+a systems and that dynamical evolution greatly controls the spectral evolution in these merger cases. Our simulations also show that a merger with very high infrared luminosity ($L_{\rm IR}$ $>$ $10^{11}$ $L_{\odot}$) is more likely to show an e(a) spectrum, which implies that spectral types can be correlated with infrared fluxes in dusty starburst galaxies. Based on these results, we discuss the origin of the evolution of k+a/a+k galaxies in distant clusters and the role merging is likely to have.

14 pages 4 figures,2001,ApJL,in press