Hubble Space T elescope (HST ) Wide Field Planetary Camera 2 images in B (F450W) and I (F814W) have been obtained for three starburst (SB) and two poststarburst (PSB) galaxies in the Coma Cluster and for three such galaxies in the cluster DC 048[52. V (F555W) and I images for an additional PSB galaxy in Coma have been extracted from the HST archive. Six of these galaxies were previously classiÐed as E/S0 on the basis of ground-based images, two as Sa, and the other as an irregular.The HST images reveal these SB/PSB galaxies to be heterogeneous in morphology. Nevertheless, a common theme is that many of them, especially the SB galaxies, tend to have centralized spiral structure that appears simply as a bright "" bulge ÏÏ on ground-based images. In addition, while some PSB galaxies exhibit distinct spiral structure, on the whole they have smoother morphologies than the SB galaxies. The morphologies and luminosity proÐles are generally consistent with substantial starbursts, in the form of centralized spiral structure (the SB galaxies), that fade into smoother morphologies (the PSB galaxies), with lingering spectroscopic evidence for past central starbursts. An important point is that the PSB galaxies retain disks ; i.e., they have not evolved into spheroidal systems.While the morphologies revealed in the HST images are heterogeneous, and thus may not Ðt well into a single picture, we see evidence in several cases that the morphologies and centralized star formation have been driven by external tidal perturbations. We discuss several physical mechanisms for inducing star formation in cluster galaxies with a view toward explaining the particular morphologies seen in the HST images.