  We present new (2004 July) G750L and G140L Space Telescope Imaging
Spectrograph (STIS) data of the H-alpha and Ly-alpha emission from supernova
remnant (SNR) 1987A. With the aid of earlier data, from Oct 1997 to Oct 2002,
we track the local evolution of Ly-alpha emission and both the local and global
evolution of H-alpha emission. In addition to emission which we can clearly
attribute to the surface of the reverse shock, we also measure comparable
emission, in both H-alpha and Ly-alpha, which appears to emerge from supernova
debris interior to the surface. New observations taken through slits positioned
slightly eastward and westward of a central slit show a departure from
cylindrical symmetry in the H-alpha surface emission. Using a combination of
old and new observations, we construct a light curve of the total H-alpha flux,
F, from the reverse shock, which has increased by a factor ~ 4 over about 8
years. However, due to large systematic uncertainties, we are unable to discern
between the two limiting behaviours of the flux - F ~ t (self-similar
expansion) and F ~ t^5 (halting of the reverse shock). Such a determination is
relevant to the question of whether the reverse shock emission will vanish in
less than about 7 years (Smith et al. 2005). Future deep, low- or
moderate-resolution spectra are essential for accomplishing this task.
