  The giant flare of 1998 August 27 from SGR 1900+14 was extraordinary in many
ways: it was the most intense flux of gamma rays ever detected from a source
outside our solar system; it was longer than any previously detected burst from
a soft gamma repeater (SGR) in our Galaxy by more than an order of magnitude;
and it showed a remarkable four-peaked, periodic pattern in hard X-rays with
the same rotation period that was found modulating soft X-rays from the star in
quiescence. The event was detected by several gamma-ray experiments in space,
including the Ulysses gamma-ray burst detector and the BeppoSAX Gamma Ray Burst
Monitor. These instruments operate in different energy ranges, and comparisons
of their measurements reveal complex patterns of spectral evolution as the
intensity varies. In this paper, we present a joint analysis of the BeppoSAX
and Ulysses data and discuss some implications of these results for the SGRs.
We also present newly-analyzed Venera/SIGNE and ISEE-3 data on the 1979 March 5
giant flare from an SGR in the Large Magellanic Cloud (SGR 0526-66), and
compare them with the August 27 event. Our results are consistent with the
hypothesis that giant flares are due to catastrophic magnetic instabilities in
highly magnetized neutron stars, or "magnetars".
